B (archetype), 98
B (definition), 99
B (section), 100
B (subsection, section B), 101
basis
columns nonsingular matrix
example CABAK, 102
common size
theorem BIS, 103
crazy vector apace
example BC, 104
definition B, 105
matrices
example BM, 106
example BSM22, 107
polynomials
example BP, 108
example BPR, 109
example BSP4, 110
example SVP4, 111
subspace of matrices
example BDM22, 112
BC (example), 113
BCS (theorem), 114
BDE (example), 115
BDM22 (example), 116
best cities
money magazine
example MBC, 117
BIS (theorem), 118
BM (example), 119
BNM (subsection, section B), 120
BNS (theorem), 121
BP (example), 122
BPR (example), 123
BRLT (example), 124
BRS (theorem), 125
BS (theorem), 126
BSCV (subsection, section B), 127
BSM22 (example), 128
BSP4 (example), 129
C (archetype), 130
C (definition), 131
C (notation), 132
C (part), 133
C (Property), 134
C (technique, section PT), 135
CABAK (example), 136
CACN (Property), 137
CAEHW (example), 138
CAF (Property), 139
canonical form
nilpotent linear transformation
example CFNLT, 140
theorem CFNLT, 141
CAV (subsection, section O), 142
Cayley-Hamilton
theorem CHT, 143
CB (section), 144
CB (theorem), 145
CBCV (example), 146
CBM (definition), 147
CBM (subsection, section CB), 148
CBP (example), 149
CC (Property), 150
CCCV (definition), 151
CCCV (notation), 152
CCM (definition), 153
CCM (example), 154
CCM (notation), 155
CCM (theorem), 156
CCN (definition), 157
CCN (notation), 158
CCN (subsection, section CNO), 159
CCRA (theorem), 160
CCRM (theorem), 161
CCT (theorem), 162
CD (subsection, section DM), 163
CD (technique, section PT), 164
CEE (subsection, section EE), 165
CELT (example), 166
CELT (subsection, section CB), 167
CEMS6 (example), 168
CF (section), 169
CFDVS (theorem), 170
CFNLT (example), 171
CFNLT (subsection, section NLT), 172
CFNLT (theorem), 173
CFV (example), 174
change of basis
between polynomials
example CBP, 175
change-of-basis
between column vectors
example CBCV, 176
matrix representation
theorem MRCB, 177
similarity
theorem SCB, 178
theorem CB, 179
change-of-basis matrix
definition CBM, 180
inverse
theorem ICBM, 181
characteristic polynomial
definition CP, 182
degree
theorem DCP, 183
size 3 matrix
example CPMS3, 184
CHT (subsection, section JCF), 185
CHT (theorem), 186
CILT (subsection, section ILT), 187
CILTI (theorem), 188
CIM (subsection, section MISLE), 189
CINM (theorem), 190
CIVLT (example), 191
CIVLT (theorem), 192
CLI (theorem), 193
CLTLT (theorem), 194
CM (definition), 195
CM (Property), 196
CM32 (example), 197
CMCN (Property), 198
CMF (Property), 199
CMI (example), 200
CMIAB (example), 201
CMVEI (theorem), 202
CN (appendix), 203
CNA (definition), 204
CNA (notation), 205
CNA (subsection, section CNO), 206
CNE (definition), 207
CNE (notation), 208
CNM (definition), 209
CNM (notation), 210
CNMB (theorem), 211
CNO (section), 212
CNS1 (example), 213
CNS2 (example), 214
CNSV (example), 215
COB (theorem), 216
coefficient matrix
definition CM, 217
nonsingular
theorem SNCM, 218
column space
as null space
theorem FS, 219
Archetype A
example CSAA, 220
Archetype B
example CSAB, 221
as null space
example CSANS, 222
as null space, Archetype G
example FSAG, 223
as row space
theorem CSRST, 224
basis
theorem BCS, 225
consistent system
theorem CSCS, 226
consistent systems
example CSMCS, 227
isomorphic to range, 228
matrix, 229
nonsingular matrix
theorem CSNM, 230
notation, 231
original columns, Archetype D
example CSOCD, 232
row operations, Archetype I
example CSROI, 233
subspace
theorem CSMS, 234
testing membership
example MCSM, 235
two computations
example CSTW, 236
column vector addition
notation, 237
column vector scalar multiplication
notation, 238
commutativity
column vectors
Property CC, 239
matrices
Property CM, 240
vectors
Property C, 241
complex m-space
example VSCV, 242
complex arithmetic
example ACN, 243
complex number
conjugate
example CSCN, 244
modulus
example MSCN, 245
complex number
conjugate
definition CCN, 246
modulus
definition MCN, 247
complex numbers
addition
definition CNA, 248
notation, 249
arithmetic properties
theorem PCNA, 250
equality
definition CNE, 251
notation, 252
multiplication
definition CNM, 253
notation, 254
complex vector space
dimension
theorem DCM, 255
composition
injective linear transformations
theorem CILTI, 256
surjective linear transformations
theorem CSLTS, 257
conjugate
addition
theorem CCRA, 258
column vector
definition CCCV, 259
matrix
definition CCM, 260
notation, 261
multiplication
theorem CCRM, 262
notation, 263
of conjugate of a matrix
theorem CCM, 264
scalar multiplication
theorem CRSM, 265
twice
theorem CCT, 266
vector addition
theorem CRVA, 267
conjugate of a vector
notation, 268
conjugation
matrix addition
theorem CRMA, 269
matrix scalar multiplication
theorem CRMSM, 270
matrix transpose
theorem MCT, 271
consistent linear system, 272
consistent linear systems
theorem CSRN, 273
consistent system
definition CS, 274
constructive proofs
technique C, 275
contradiction
technique CD, 276
contrapositive
technique CP, 277
converse
technique CV, 278
coordinates
orthonormal basis
theorem COB, 279
coordinatization
linear combination of matrices
example CM32, 280
linear independence
theorem CLI, 281
orthonormal basis
example CROB3, 282
example CROB4, 283
spanning sets
theorem CSS, 284
coordinatization principle, 285
coordinatizing
polynomials
example CP2, 286
COV (example), 287
COV (subsection, section LDS), 288
CP (definition), 289
CP (subsection, section VR), 290
CP (technique, section PT), 291
CP2 (example), 292
CPMS3 (example), 293
CPSM (theorem), 294
crazy vector space
example CVSR, 295
properties
example PCVS, 296
CRMA (theorem), 297
CRMSM (theorem), 298
CRN (theorem), 299
CROB3 (example), 300
CROB4 (example), 301
CRS (section), 302
CRS (subsection, section FS), 303
CRSM (theorem), 304
CRVA (theorem), 305
CS (definition), 306
CS (example), 307
CS (subsection, section TSS), 308
CSAA (example), 309
CSAB (example), 310
CSANS (example), 311
CSCN (example), 312
CSCS (theorem), 313
CSIP (example), 314
CSLT (subsection, section SLT), 315
CSLTS (theorem), 316
CSM (definition), 317
CSM (notation), 318
CSMCS (example), 319
CSMS (theorem), 320
CSNM (subsection, section CRS), 321
CSNM (theorem), 322
CSOCD (example), 323
CSRN (theorem), 324
CSROI (example), 325
CSRST (diagram), 326
CSRST (theorem), 327
CSS (theorem), 328
CSSE (subsection, section CRS), 329
CSSOC (subsection, section CRS), 330
CSTW (example), 331
CTD (subsection, section TD), 332
CTLT (example), 333
CUMOS (theorem), 334
curve fitting
polynomial through 5 points
example PTFP, 335
CV (definition), 336
CV (notation), 337
CV (technique, section PT), 338
CVA (definition), 339
CVA (notation), 340
CVC (notation), 341
CVE (definition), 342
CVE (notation), 343
CVS (example), 344
CVS (subsection, section VR), 345
CVSM (definition), 346
CVSM (example), 347
CVSM (notation), 348
CVSR (example), 349
D (acronyms, section PDM), 350
D (archetype), 351
D (chapter), 352
D (definition), 353
D (notation), 354
D (section), 355
D (subsection, section D), 356
D (subsection, section SD), 357
D (technique, section PT), 358
D33M (example), 359
DAB (example), 360
DC (example), 361
DC (technique, section PT), 362
DC (theorem), 363
DCM (theorem), 364
DCN (Property), 365
DCP (theorem), 366
DD (subsection, section DM), 367
DEC (theorem), 368
decomposition
technique DC, 369
DED (theorem), 370
definition
A, 371
AM, 372
AME, 373
B, 374
C, 375
CBM, 376
CCCV, 377
CCM, 378
CCN, 379
CM, 380
CNA, 381
CNE, 382
CNM, 383
CP, 384
CS, 385
CSM, 386
CV, 387
CVA, 388
CVE, 389
CVSM, 390
D, 391
DIM, 392
DM, 393
DS, 394
DZM, 395
EEF, 396
EELT, 397
EEM, 398
ELEM, 399
EM, 400
EO, 401
ES, 402
ESYS, 403
F, 404
GES, 405
GEV, 406
GME, 407
HI, 408
HID, 409
HM, 410
HP, 411
HS, 412
IDLT, 413
IDV, 414
IE, 415
ILT, 416
IM, 417
IMP, 418
IP, 419
IS, 420
IVLT, 421
IVS, 422
JB, 423
JCF, 424
KLT, 425
LC, 426
LCCV, 427
LI, 428
LICV, 429
LNS, 430
LSS, 431
LT, 432
LTA, 433
LTC, 434
LTM, 435
LTR, 436
LTSM, 437
M, 438
MA, 439
MCN, 440
ME, 441
MI, 442
MM, 443
MR, 444
MRLS, 445
MSM, 446
MVP, 447
NLT, 448
NM, 449
NOLT, 450
NOM, 451
NRML, 452
NSM, 453
NV, 454
ONS, 455
OSV, 456
OV, 457
PI, 458
PSM, 459
REM, 460
RLD, 461
RLDCV, 462
RLT, 463
RO, 464
ROLT, 465
ROM, 466
RR, 467
RREF, 468
RSM, 469
S, 470
SC, 471
SE, 472
SET, 473
SI, 474
SIM, 475
SLE, 476
SLT, 477
SM, 478
SOLV, 479
SQM, 480
SRM, 481
SS, 482
SSCV, 483
SSET, 484
SSLE, 485
SSSLE, 486
SU, 487
SUV, 488
SV, 489
SYM, 490
T, 491
technique D, 492
TM, 493
TS, 494
TSHSE, 495
TSVS, 496
UM, 497
UTM, 498
VM, 499
VOC, 500
VR, 501
VS, 502
VSCV, 503
VSM, 504
ZCV, 505
ZM, 506
DEHD (example), 507
DEM (theorem), 508
DEMMM (theorem), 509
DEMS5 (example), 510
DER (theorem), 511
DERC (theorem), 512
determinant
computed two ways
example TCSD, 513
definition DM, 514
equal rows or columns
theorem DERC, 515
expansion, columns
theorem DEC, 516
expansion, rows
theorem DER, 517
identity matrix
theorem DIM, 518
matrix multiplication
theorem DRMM, 519
nonsingular matrix, 520
notation, 521
row or column multiple
theorem DRCM, 522
row or column swap
theorem DRCS, 523
size 2 matrix
theorem DMST, 524
size 3 matrix
example D33M, 525
transpose
theorem DT, 526
via row operations
example DRO, 527
zero
theorem SMZD, 528
zero row or column
theorem DZRC, 529
zero versus nonzero
example ZNDAB, 530
determinant, upper triangular matrix
example DUTM, 531
determinants
elementary matrices
theorem DEMMM, 532
DF (Property), 533
DF (subsection, section CF), 534
DFS (subsection, section PD), 535
DFS (theorem), 536
DGES (theorem), 537
diagonal matrix
definition DIM, 538
diagonalizable
definition DZM, 539
distinct eigenvalues
example DEHD, 540
theorem DED, 541
full eigenspaces
theorem DMFE, 542
not
example NDMS4, 543
diagonalizable matrix
high power
example HPDM, 544
diagonalization
Archetype B
example DAB, 545
criteria
theorem DC, 546
example DMS3, 547
diagram
CSRST, 548
DLTA, 549
DLTM, 550
DTSLS, 551
FTMR, 552
FTMRA, 553
GLT, 554
ILT, 555
MRCLT, 556
NILT, 557
DIM (definition), 558
DIM (theorem), 559
dimension
crazy vector space
example DC, 560
definition D, 561
notation, 562
polynomial subspace
example DSP4, 563
proper subspaces
theorem PSSD, 564
subspace
example DSM22, 565
direct sum
decomposing zero vector
theorem DSZV, 566
definition DS, 567
dimension
theorem DSD, 568
example SDS, 569
from a basis
theorem DSFB, 570
from one subspace
theorem DSFOS, 571
notation, 572
zero intersection
theorem DSZI, 573
direct sums
linear independence
theorem DSLI, 574
repeated
theorem RDS, 575
distributivity
complex numbers
Property DCN, 576
field
Property DF, 577
distributivity, matrix addition
matrices
Property DMAM, 578
distributivity, scalar addition
column vectors
Property DSAC, 579
matrices
Property DSAM, 580
vectors
Property DSA, 581
distributivity, vector addition
column vectors
Property DVAC, 582
vectors
Property DVA, 583
DLDS (theorem), 584
DLTA (diagram), 585
DLTM (diagram), 586
DM (definition), 587
DM (notation), 588
DM (section), 589
DM (theorem), 590
DMAM (Property), 591
DMFE (theorem), 592
DMHP (subsection, section HP), 593
DMHP (theorem), 594
DMMP (theorem), 595
DMS3 (example), 596
DMST (theorem), 597
DNLT (theorem), 598
DNMMM (subsection, section PDM), 599
DP (theorem), 600
DRCM (theorem), 601
DRCMA (theorem), 602
DRCS (theorem), 603
DRMM (theorem), 604
DRO (example), 605
DRO (subsection, section PDM), 606
DROEM (subsection, section PDM), 607
DS (definition), 608
DS (notation), 609
DS (subsection, section PD), 610
DSA (Property), 611
DSAC (Property), 612
DSAM (Property), 613
DSD (theorem), 614
DSFB (theorem), 615
DSFOS (theorem), 616
DSLI (theorem), 617
DSM22 (example), 618
DSP4 (example), 619
DSZI (theorem), 620
DSZV (theorem), 621
DT (theorem), 622
DTSLS (diagram), 623
DUTM (example), 624
DVA (Property), 625
DVAC (Property), 626
DVM (theorem), 627
DVS (subsection, section D), 628
DZM (definition), 629
DZRC (theorem), 630
E (acronyms, section SD), 631
E (archetype), 632
E (chapter), 633
E (technique, section PT), 634
E.SAGE (computation, section SAGE), 635
ECEE (subsection, section EE), 636
EDELI (theorem), 637
EDYES (theorem), 638
EE (section), 639
EEE (subsection, section EE), 640
EEF (definition), 641
EEF (subsection, section FS), 642
EELT (definition), 643
EELT (subsection, section CB), 644
EEM (definition), 645
EEM (subsection, section EE), 646
EEMAP (theorem), 647
EENS (example), 648
EER (theorem), 649
EESR (theorem), 650
EHM (subsection, section PEE), 651
eigenspace
as null space
theorem EMNS, 652
definition EM, 653
invariant subspace
theorem EIS, 654
subspace
theorem EMS, 655
eigenspaces
sage, 656
eigenvalue
algebraic multiplicity
definition AME, 657
notation, 658
complex
example CEMS6, 659
definition EEM, 660
existence
example CAEHW, 661
theorem EMHE, 662
geometric multiplicity
definition GME, 663
notation, 664
index, 665
linear transformation
definition EELT, 666
multiplicities
example EMMS4, 667
power
theorem EOMP, 668
root of characteristic polynomial
theorem EMRCP, 669
scalar multiple
theorem ESMM, 670
symmetric matrix
example ESMS4, 671
zero
theorem SMZE, 672
eigenvalues
building desired
example BDE, 673
complex, of a linear transformation
example CELT, 674
conjugate pairs
theorem ERMCP, 675
distinct
example DEMS5, 676
example SEE, 677
Hermitian matrices
theorem HMRE, 678
inverse
theorem EIM, 679
maximum number
theorem MNEM, 680
multiplicities
example HMEM5, 681
theorem ME, 682
number
theorem NEM, 683
of a polynomial
theorem EPM, 684
size 3 matrix
example EMS3, 685
example ESMS3, 686
transpose
theorem ETM, 687
eigenvalues, eigenvectors
vector, matrix representations
theorem EER, 688
eigenvector, 689
linear transformation, 690
eigenvectors, 691
conjugate pairs, 692
Hermitian matrices
theorem HMOE, 693
linear transformation
example ELTBM, 694
example ELTBP, 695
linearly independent
theorem EDELI, 696
of a linear transformation
example ELTT, 697
EILT (subsection, section ILT), 698
EIM (theorem), 699
EIS (example), 700
EIS (theorem), 701
ELEM (definition), 702
ELEM (notation), 703
elementary matrices
definition ELEM, 704
determinants
theorem DEM, 705
nonsingular
theorem EMN, 706
notation, 707
row operations
example EMRO, 708
theorem EMDRO, 709
ELIS (theorem), 710
ELTBM (example), 711
ELTBP (example), 712
ELTT (example), 713
EM (definition), 714
EM (subsection, section DM), 715
EMDRO (theorem), 716
EMHE (theorem), 717
EMMS4 (example), 718
EMMVP (theorem), 719
EMN (theorem), 720
EMNS (theorem), 721
EMP (theorem), 722
empty set, 723
notation, 724
EMRCP (theorem), 725
EMRO (example), 726
EMS (theorem), 727
EMS3 (example), 728
ENLT (theorem), 729
EO (definition), 730
EOMP (theorem), 731
EOPSS (theorem), 732
EPM (theorem), 733
EPSM (theorem), 734
equal matrices
via equal matrix-vector products
theorem EMMVP, 735
equation operations
definition EO, 736
theorem EOPSS, 737
equivalence statements
technique E, 738
equivalences
technique ME, 739
equivalent systems
definition ESYS, 740
ERMCP (theorem), 741
ES (definition), 742
ES (notation), 743
ESEO (subsection, section SSLE), 744
ESLT (subsection, section SLT), 745
ESMM (theorem), 746
ESMS3 (example), 747
ESMS4 (example), 748
ESYS (definition), 749
ETM (theorem), 750
EVS (subsection, section VS), 751
example
AALC, 752
ABLC, 753
ABS, 754
ACN, 755
AHSAC, 756
AIVLT, 757
ALT, 758
ALTMM, 759
AM, 760
AMAA, 761
ANILT, 762
ANM, 763
AOS, 764
ASC, 765
AVR, 766
BC, 767
BDE, 768
BDM22, 769
BM, 770
BP, 771
BPR, 772
BRLT, 773
BSM22, 774
BSP4, 775
CABAK, 776
CAEHW, 777
CBCV, 778
CBP, 779
CCM, 780
CELT, 781
CEMS6, 782
CFNLT, 783
CFV, 784
CIVLT, 785
CM32, 786
CMI, 787
CMIAB, 788
CNS1, 789
CNS2, 790
CNSV, 791
COV, 792
CP2, 793
CPMS3, 794
CROB3, 795
CROB4, 796
CS, 797
CSAA, 798
CSAB, 799
CSANS, 800
CSCN, 801
CSIP, 802
CSMCS, 803
CSOCD, 804
CSROI, 805
CSTW, 806
CTLT, 807
CVS, 808
CVSM, 809
CVSR, 810
D33M, 811
DAB, 812
DC, 813
DEHD, 814
DEMS5, 815
DMS3, 816
DRO, 817
DSM22, 818
DSP4, 819
DUTM, 820
EENS, 821
EIS, 822
ELTBM, 823
ELTBP, 824
ELTT, 825
EMMS4, 826
EMRO, 827
EMS3, 828
ESMS3, 829
ESMS4, 830
FDV, 831
FF8, 832
FRAN, 833
FS1, 834
FS2, 835
FSAG, 836
FSCF, 837
GE4, 838
GE6, 839
GENR6, 840
GSTV, 841
HISAA, 842
HISAD, 843
HMEM5, 844
HP, 845
HPDM, 846
HUSAB, 847
IAP, 848
IAR, 849
IAS, 850
IAV, 851
ILTVR, 852
IM, 853
IM11, 854
IS, 855
ISJB, 856
ISMR4, 857
ISMR6, 858
ISSI, 859
IVSAV, 860
JB4, 861
JCF10, 862
KPNLT, 863
KVMR, 864
LCM, 865
LDCAA, 866
LDHS, 867
LDP4, 868
LDRN, 869
LDS, 870
LIC, 871
LICAB, 872
LIHS, 873
LIM32, 874
LINSB, 875
LIP4, 876
LIS, 877
LLDS, 878
LNS, 879
LTDB1, 880
LTDB2, 881
LTDB3, 882
LTM, 883
LTPM, 884
LTPP, 885
LTRGE, 886
MA, 887
MBC, 888
MCSM, 889
MFLT, 890
MI, 891
MIVS, 892
MMNC, 893
MNSLE, 894
MOLT, 895
MPMR, 896
MRBE, 897
MRCM, 898
MSCN, 899
MSM, 900
MTV, 901
MWIAA, 902
NDMS4, 903
NIAO, 904
NIAQ, 905
NIAQR, 906
NIDAU, 907
NJB5, 908
NKAO, 909
NLT, 910
NM, 911
NM62, 912
NM64, 913
NM83, 914
NRREF, 915
NSAO, 916
NSAQ, 917
NSAQR, 918
NSC2A, 919
NSC2S, 920
NSC2Z, 921
NSDAT, 922
NSDS, 923
NSE, 924
NSEAI, 925
NSLE, 926
NSLIL, 927
NSNM, 928
NSR, 929
NSS, 930
OLTTR, 931
ONFV, 932
ONTV, 933
OSGMD, 934
OSMC, 935
PCVS, 936
PM, 937
PSHS, 938
PTFP, 939
PTM, 940
PTMEE, 941
RAO, 942
RES, 943
RNM, 944
RNSM, 945
ROD2, 946
ROD4, 947
RREF, 948
RREFN, 949
RRTI, 950
RS, 951
RSAI, 952
RSB, 953
RSC4, 954
RSC5, 955
RSNS, 956
RSREM, 957
RVMR, 958
S, 959
SAA, 960
SAB, 961
SABMI, 962
SAE, 963
SAN, 964
SAR, 965
SAV, 966
SC, 967
SC3, 968
SCAA, 969
SCAB, 970
SCAD, 971
SDS, 972
SEE, 973
SEEF, 974
SETM, 975
SI, 976
SM2Z7, 977
SM32, 978
SMLT, 979
SMS3, 980
SMS5, 981
SP4, 982
SPIAS, 983
SRR, 984
SS, 985
SS6W, 986
SSC, 987
SSET, 988
SSM22, 989
SSNS, 990
SSP, 991
SSP4, 992
STLT, 993
STNE, 994
SU, 995
SUVOS, 996
SVP4, 997
SYM, 998
TCSD, 999
TD4, 1000
TDEE6, 1001
TDSSE, 1002
TIS, 1003
TIVS, 1004
TKAP, 1005
TLC, 1006
TM, 1007
TMP, 1008
TOV, 1009
TREM, 1010
TTS, 1011
UM3, 1012
UPM, 1013
US, 1014
USR, 1015
VA, 1016
VESE, 1017
VFS, 1018
VFSAD, 1019
VFSAI, 1020
VFSAL, 1021
VM4, 1022
VRC4, 1023
VRP2, 1024
VSCV, 1025
VSF, 1026
VSIM5, 1027
VSIS, 1028
VSM, 1029
VSP, 1030
VSPUD, 1031
VSS, 1032
ZNDAB, 1033
EXC (subsection, section B), 1034
EXC (subsection, section CB), 1035
EXC (subsection, section CF), 1036
EXC (subsection, section CRS), 1037
EXC (subsection, section D), 1038
EXC (subsection, section DM), 1039
EXC (subsection, section EE), 1040
EXC (subsection, section F), 1041
EXC (subsection, section FS), 1042
EXC (subsection, section HP), 1043
EXC (subsection, section HSE), 1044
EXC (subsection, section ILT), 1045
EXC (subsection, section IS), 1046
EXC (subsection, section IVLT), 1047
EXC (subsection, section LC), 1048
EXC (subsection, section LDS), 1049
EXC (subsection, section LI), 1050
EXC (subsection, section LISS), 1051
EXC (subsection, section LT), 1052
EXC (subsection, section MINM), 1053
EXC (subsection, section MISLE), 1054
EXC (subsection, section MM), 1055
EXC (subsection, section MO), 1056
EXC (subsection, section MR), 1057
EXC (subsection, section NM), 1058
EXC (subsection, section O), 1059
EXC (subsection, section PD), 1060
EXC (subsection, section PDM), 1061
EXC (subsection, section PEE), 1062
EXC (subsection, section PSM), 1063
EXC (subsection, section RREF), 1064
EXC (subsection, section S), 1065
EXC (subsection, section SD), 1066
EXC (subsection, section SLT), 1067
EXC (subsection, section SS), 1068
EXC (subsection, section SSLE), 1069
EXC (subsection, section T), 1070
EXC (subsection, section TSS), 1071
EXC (subsection, section VO), 1072
EXC (subsection, section VR), 1073
EXC (subsection, section VS), 1074
EXC (subsection, section WILA), 1075
extended echelon form
submatrices
example SEEF, 1076
extended reduced row-echelon form
properties
theorem PEEF, 1077
F (archetype), 1078
F (definition), 1079
F (section), 1080
F (subsection, section F), 1081
FDV (example), 1082
FF (subsection, section F), 1083
FF8 (example), 1084
Fibonacci sequence
example FSCF, 1085
field
definition F, 1086
FIMP (theorem), 1087
finite field
size 8
example FF8, 1088
four subsets
example FS1, 1089
example FS2, 1090
four subspaces
dimension
theorem DFS, 1091
FRAN (example), 1092
free variables
example CFV, 1093
free variables, number
theorem FVCS, 1094
free, independent variables
example FDV, 1095
FS (section), 1096
FS (subsection, section FS), 1097
FS (subsection, section SD), 1098
FS (theorem), 1099
FS1 (example), 1100
FS2 (example), 1101
FSAG (example), 1102
FSCF (example), 1103
FTMR (diagram), 1104
FTMR (theorem), 1105
FTMRA (diagram), 1106
FV (subsection, section TSS), 1107
FVCS (theorem), 1108
G (archetype), 1109
G (theorem), 1110
GE4 (example), 1111
GE6 (example), 1112
GEE (subsection, section IS), 1113
GEK (theorem), 1114
generalized eigenspace
as kernel
theorem GEK, 1115
definition GES, 1116
dimension
theorem DGES, 1117
dimension 4 domain
example GE4, 1118
dimension 6 domain
example GE6, 1119
invariant subspace
theorem GESIS, 1120
nilpotent restriction
theorem RGEN, 1121
nilpotent restrictions, dimension 6 domain
example GENR6, 1122
notation, 1123
generalized eigenspace decomposition
theorem GESD, 1124
generalized eigenvector
definition GEV, 1125
GENR6 (example), 1126
GES (definition), 1127
GES (notation), 1128
GESD (subsection, section JCF), 1129
GESD (theorem), 1130
GESIS (theorem), 1131
GEV (definition), 1132
GFDL (appendix), 1133
GLT (diagram), 1134
GME (definition), 1135
GME (notation), 1136
goldilocks
theorem G, 1137
Gram-Schmidt
column vectors
theorem GSP, 1138
three vectors
example GSTV, 1139
gram-schmidt
mathematica, 1140
GS (technique, section PT), 1141
GSP (subsection, section O), 1142
GSP (theorem), 1143
GSP.MMA (computation, section MMA), 1144
GSTV (example), 1145
GT (subsection, section PD), 1146
H (archetype), 1147
Hadamard Identity
notation, 1148
Hadamard identity
definition HID, 1149
Hadamard Inverse
notation, 1150
Hadamard inverse
definition HI, 1151
Hadamard Product
Diagonalizable Matrices
theorem DMHP, 1152
notation, 1153
Hadamard product
commutativity
theorem HPC, 1154
definition HP, 1155
diagonal matrices
theorem DMMP, 1156
distributivity
theorem HPDAA, 1157
example HP, 1158
identity
theorem HPHID, 1159
inverse
theorem HPHI, 1160
scalar matrix multiplication
theorem HPSMM, 1161
hermitian
definition HM, 1162
Hermitian matrix
inner product
theorem HMIP, 1163
HI (definition), 1164
HI (notation), 1165
HID (definition), 1166
HID (notation), 1167
HISAA (example), 1168
HISAD (example), 1169
HM (definition), 1170
HM (subsection, section MM), 1171
HMEM5 (example), 1172
HMIP (theorem), 1173
HMOE (theorem), 1174
HMRE (theorem), 1175
HMVEI (theorem), 1176
homogeneous system
Archetype C
example AHSAC, 1177
consistent
theorem HSC, 1178
definition HS, 1179
infinitely many solutions
theorem HMVEI, 1180
homogeneous systems
linear independence, 1181
HP (definition), 1182
HP (example), 1183
HP (notation), 1184
HP (section), 1185
HPC (theorem), 1186
HPDAA (theorem), 1187
HPDM (example), 1188
HPHI (theorem), 1189
HPHID (theorem), 1190
HPSMM (theorem), 1191
HS (definition), 1192
HSC (theorem), 1193
HSE (section), 1194
HUSAB (example), 1195
I (archetype), 1196
I (technique, section PT), 1197
IAP (example), 1198
IAR (example), 1199
IAS (example), 1200
IAV (example), 1201
ICBM (theorem), 1202
ICLT (theorem), 1203
identities
technique PI, 1204
identity matrix
determinant, 1205
example IM, 1206
notation, 1207
IDLT (definition), 1208
IDV (definition), 1209
IE (definition), 1210
IE (notation), 1211
IFDVS (theorem), 1212
IILT (theorem), 1213
ILT (definition), 1214
ILT (diagram), 1215
ILT (section), 1216
ILTB (theorem), 1217
ILTD (subsection, section ILT), 1218
ILTD (theorem), 1219
ILTIS (theorem), 1220
ILTLI (subsection, section ILT), 1221
ILTLI (theorem), 1222
ILTLT (theorem), 1223
ILTVR (example), 1224
IM (definition), 1225
IM (example), 1226
IM (notation), 1227
IM (subsection, section MISLE), 1228
IM11 (example), 1229
IMILT (theorem), 1230
IMP (definition), 1231
IMR (theorem), 1232
inconsistent linear systems
theorem ISRN, 1233
independent, dependent variables
definition IDV, 1234
indesxstring
example SM2Z7, 1235
example SSET, 1236
index
eigenvalue
definition IE, 1237
notation, 1238
indexstring
theorem DRCMA, 1239
theorem OBUTR, 1240
theorem UMCOB, 1241
induction
technique I, 1242
infinite solution set
example ISSI, 1243
infinite solutions, 3 × 4
example IS, 1244
injective
example IAP, 1245
example IAR, 1246
not
example NIAO, 1247
example NIAQ, 1248
example NIAQR, 1249
not, by dimension
example NIDAU, 1250
polynomials to matrices
example IAV, 1251
injective linear transformation
bases
theorem ILTB, 1252
injective linear transformations
dimension
theorem ILTD, 1253
inner product
anti-commutative
theorem IPAC, 1254
example CSIP, 1255
norm
theorem IPN, 1256
notation, 1257
positive
theorem PIP, 1258
scalar multiplication
theorem IPSM, 1259
vector addition
theorem IPVA, 1260
integers
mod p
definition IMP, 1261
mod p, field
theorem FIMP, 1262
mod 11
example IM11, 1263
interpolating polynomial
theorem IP, 1264
invariant subspace
definition IS, 1265
eigenspace, 1266
eigenspaces
example EIS, 1267
example TIS, 1268
Jordan block
example ISJB, 1269
kernels of powers
theorem KPIS, 1270
inverse
composition of linear transformations
theorem ICLT, 1271
example CMI, 1272
example MI, 1273
notation, 1274
of a matrix, 1275
invertible linear transformation
defined by invertible matrix
theorem IMILT, 1276
invertible linear transformations
composition
theorem CIVLT, 1277
computing
example CIVLT, 1278
IP (definition), 1279
IP (notation), 1280
IP (subsection, section O), 1281
IP (theorem), 1282
IPAC (theorem), 1283
IPN (theorem), 1284
IPSM (theorem), 1285
IPVA (theorem), 1286
IS (definition), 1287
IS (example), 1288
IS (section), 1289
IS (subsection, section IS), 1290
ISJB (example), 1291
ISMR4 (example), 1292
ISMR6 (example), 1293
isomorphic
multiple vector spaces
example MIVS, 1294
vector spaces
example IVSAV, 1295
isomorphic vector spaces
dimension
theorem IVSED, 1296
example TIVS, 1297
ISRN (theorem), 1298
ISSI (example), 1299
ITMT (theorem), 1300
IV (subsection, section IVLT), 1301
IVLT (definition), 1302
IVLT (section), 1303
IVLT (subsection, section IVLT), 1304
IVLT (subsection, section MR), 1305
IVS (definition), 1306
IVSAV (example), 1307
IVSED (theorem), 1308
J (archetype), 1309
JB (definition), 1310
JB (notation), 1311
JB4 (example), 1312
JCF (definition), 1313
JCF (section), 1314
JCF (subsection, section JCF), 1315
JCF10 (example), 1316
JCFLT (theorem), 1317
Jordan block
definition JB, 1318
nilpotent
theorem NJB, 1319
notation, 1320
size 4
example JB4, 1321
Jordan canonical form
definition JCF, 1322
size 10
example JCF10, 1323
K (archetype), 1324
kernel
injective linear transformation
theorem KILT, 1325
isomorphic to null space
theorem KNSI, 1326
linear transformation
example NKAO, 1327
notation, 1328
of a linear transformation
definition KLT, 1329
pre-image, 1330
subspace
theorem KLTS, 1331
trivial
example TKAP, 1332
via matrix representation
example KVMR, 1333
KILT (theorem), 1334
KLT (definition), 1335
KLT (notation), 1336
KLT (subsection, section ILT), 1337
KLTS (theorem), 1338
KNSI (theorem), 1339
KPI (theorem), 1340
KPIS (theorem), 1341
KPLT (theorem), 1342
KPNLT (example), 1343
KPNLT (theorem), 1344
KVMR (example), 1345
L (archetype), 1346
L (technique, section PT), 1347
LA (subsection, section WILA), 1348
LC (definition), 1349
LC (section), 1350
LC (subsection, section LC), 1351
LC (technique, section PT), 1352
LCCV (definition), 1353
LCM (example), 1354
LDCAA (example), 1355
LDHS (example), 1356
LDP4 (example), 1357
LDRN (example), 1358
LDS (example), 1359
LDS (section), 1360
LDSS (subsection, section LDS), 1361
least squares
minimizes residuals
theorem LSMR, 1362
least squares solution
definition LSS, 1363
left null space
as row space, 1364
definition LNS, 1365
example LNS, 1366
notation, 1367
subspace
theorem LNSMS, 1368
lemma
technique LC, 1369
LI (definition), 1370
LI (section), 1371
LI (subsection, section LISS), 1372
LIC (example), 1373
LICAB (example), 1374
LICV (definition), 1375
LIHS (example), 1376
LIM32 (example), 1377
linear combination
system of equations
example ABLC, 1378
definition LC, 1379
definition LCCV, 1380
example TLC, 1381
linear transformation, 1382
matrices
example LCM, 1383
system of equations
example AALC, 1384
linear combinations
solutions to linear systems
theorem SLSLC, 1385
linear dependence
more vectors than size
theorem MVSLD, 1386
linear independence
definition LI, 1387
definition LICV, 1388
homogeneous systems
theorem LIVHS, 1389
injective linear transformation
theorem ILTLI, 1390
matrices
example LIM32, 1391
orthogonal, 1392
r and n
theorem LIVRN, 1393
linear solve
mathematica, 1394
sage, 1395
linear system
consistent
theorem RCLS, 1396
matrix representation
definition MRLS, 1397
notation, 1398
linear systems
notation
example MNSLE, 1399
example NSLE, 1400
linear transformation
polynomials to polynomials
example LTPP, 1401
addition
definition LTA, 1402
theorem MLTLT, 1403
theorem SLTLT, 1404
as matrix multiplication
example ALTMM, 1405
basis of range
example BRLT, 1406
checking
example ALT, 1407
composition
definition LTC, 1408
theorem CLTLT, 1409
defined by a matrix
example LTM, 1410
defined on a basis
example LTDB1, 1411
example LTDB2, 1412
example LTDB3, 1413
theorem LTDB, 1414
definition LT, 1415
identity
definition IDLT, 1416
injection
definition ILT, 1417
inverse
theorem ILTLT, 1418
inverse of inverse
theorem IILT, 1419
invertible
definition IVLT, 1420
example AIVLT, 1421
invertible, injective and surjective
theorem ILTIS, 1422
Jordan canonical form
theorem JCFLT, 1423
kernels of powers
theorem KPLT, 1424
linear combination
theorem LTLC, 1425
matrix of, 1426
example MFLT, 1427
example MOLT, 1428
not
example NLT, 1429
not invertible
example ANILT, 1430
notation, 1431
polynomials to matrices
example LTPM, 1432
rank plus nullity
theorem RPNDD, 1433
restriction
definition LTR, 1434
notation, 1435
scalar multiple
example SMLT, 1436
scalar multiplication
definition LTSM, 1437
spanning range
theorem SSRLT, 1438
sum
example STLT, 1439
surjection
definition SLT, 1440
vector space of, 1441
zero vector
theorem LTTZZ, 1442
linear transformation inverse
via matrix representation
example ILTVR, 1443
linear transformation restriction
on generalized eigenspace
example LTRGE, 1444
linear transformations
compositions
example CTLT, 1445
from matrices
theorem MBLT, 1446
linearly dependent
r < n
example LDRN, 1447
via homogeneous system
example LDHS, 1448
linearly dependent columns
Archetype A
example LDCAA, 1449
linearly dependent set
example LDS, 1450
linear combinations within
theorem DLDS, 1451
polynomials
example LDP4, 1452
linearly independent
crazy vector space
example LIC, 1453
extending sets
theorem ELIS, 1454
polynomials
example LIP4, 1455
via homogeneous system
example LIHS, 1456
linearly independent columns
Archetype B
example LICAB, 1457
linearly independent set
example LIS, 1458
example LLDS, 1459
LINM (subsection, section LI), 1460
LINSB (example), 1461
LIP4 (example), 1462
LIS (example), 1463
LISS (section), 1464
LISV (subsection, section LI), 1465
LIVHS (theorem), 1466
LIVRN (theorem), 1467
LLDS (example), 1468
LNS (definition), 1469
LNS (example), 1470
LNS (notation), 1471
LNS (subsection, section FS), 1472
LNSMS (theorem), 1473
lower triangular matrix
definition LTM, 1474
LS.MMA (computation, section MMA), 1475
LS.SAGE (computation, section SAGE), 1476
LSMR (theorem), 1477
LSS (definition), 1478
LT (acronyms, section IVLT), 1479
LT (chapter), 1480
LT (definition), 1481
LT (notation), 1482
LT (section), 1483
LT (subsection, section LT), 1484
LTA (definition), 1485
LTC (definition), 1486
LTC (subsection, section LT), 1487
LTDB (theorem), 1488
LTDB1 (example), 1489
LTDB2 (example), 1490
LTDB3 (example), 1491
LTLC (subsection, section LT), 1492
LTLC (theorem), 1493
LTM (definition), 1494
LTM (example), 1495
LTPM (example), 1496
LTPP (example), 1497
LTR (definition), 1498
LTR (notation), 1499
LTRGE (example), 1500
LTSM (definition), 1501
LTTZZ (theorem), 1502
M (acronyms, section FS), 1503
M (archetype), 1504
M (chapter), 1505
M (definition), 1506
M (notation), 1507
MA (definition), 1508
MA (example), 1509
MA (notation), 1510
MACN (Property), 1511
MAF (Property), 1512
MAP (subsection, section SVD), 1513
mathematica
gram-schmidt (computation), 1514
linear solve (computation), 1515
matrix entry (computation), 1516
matrix inverse (computation), 1517
matrix multiplication (computation), 1518
null space (computation), 1519
row reduce (computation), 1520
transpose of a matrix (computation), 1521
vector form of solutions (computation), 1522
vector linear combinations (computation), 1523
mathematical language
technique L, 1524
matrix
addition
definition MA, 1525
notation, 1526
augmented
definition AM, 1527
column space
definition CSM, 1528
complex conjugate
example CCM, 1529
definition M, 1530
equality
definition ME, 1531
notation, 1532
example AM, 1533
identity
definition IM, 1534
inverse
definition MI, 1535
nonsingular
definition NM, 1536
notation, 1537
of a linear transformation
theorem MLTCV, 1538
product
example PTM, 1539
example PTMEE, 1540
product with vector
definition MVP, 1541
rectangular, 1542
row space
definition RSM, 1543
scalar multiplication
definition MSM, 1544
notation, 1545
singular, 1546
square
definition SQM, 1547
submatrices
example SS, 1548
submatrix
definition SM, 1549
symmetric
definition SYM, 1550
transpose
definition TM, 1551
unitary
definition UM, 1552
unitary is invertible
theorem UMI, 1553
zero
definition ZM, 1554
matrix addition
example MA, 1555
matrix components
notation, 1556
matrix entry
mathematica, 1557
sage, 1558
ti83, 1559
ti86, 1560
matrix inverse
Archetype B, 1561
computation
theorem CINM, 1562
mathematica, 1563
nonsingular matrix
theorem NI, 1564
of a matrix inverse
theorem MIMI, 1565
one-sided
theorem OSIS, 1566
product
theorem SS, 1567
sage, 1568
scalar multiple
theorem MISM, 1569
size 2 matrices
theorem TTMI, 1570
transpose
theorem MIT, 1571
uniqueness
theorem MIU, 1572
matrix multiplication
adjoints
theorem MMAD, 1573
associativity
theorem MMA, 1574
complex conjugation
theorem MMCC, 1575
definition MM, 1576
distributivity
theorem MMDAA, 1577
entry-by-entry
theorem EMP, 1578
identity matrix
theorem MMIM, 1579
inner product
theorem MMIP, 1580
mathematica, 1581
noncommutative
example MMNC, 1582
scalar matrix multiplication
theorem MMSMM, 1583
systems of linear equations
theorem SLEMM, 1584
transposes
theorem MMT, 1585
zero matrix
theorem MMZM, 1586
matrix product
as composition of linear transformations
example MPMR, 1587
matrix representation
basis of eigenvectors
example MRBE, 1588
composition of linear transformations
theorem MRCLT, 1589
definition MR, 1590
invertible
theorem IMR, 1591
multiple of a linear transformation
theorem MRMLT, 1592
notation, 1593
restriction to generalized eigenspace
theorem MRRGE, 1594
sum of linear transformations
theorem MRSLT, 1595
theorem FTMR, 1596
upper triangular
theorem UTMR, 1597
matrix representations
converting with change-of-basis
example MRCM, 1598
example OLTTR, 1599
matrix scalar multiplication
example MSM, 1600
matrix vector space
dimension
theorem DM, 1601
matrix-adjoint product
eigenvalues, eigenvectors
theorem EEMAP, 1602
matrix-vector product
example MTV, 1603
notation, 1604
MBC (example), 1605
MBLT (theorem), 1606
MC (notation), 1607
MCC (subsection, section MO), 1608
MCCN (Property), 1609
MCF (Property), 1610
MCN (definition), 1611
MCN (subsection, section CNO), 1612
MCSM (example), 1613
MCT (theorem), 1614
MD (chapter), 1615
ME (definition), 1616
ME (notation), 1617
ME (subsection, section PEE), 1618
ME (technique, section PT), 1619
ME (theorem), 1620
ME.MMA (computation, section MMA), 1621
ME.SAGE (computation, section SAGE), 1622
ME.TI83 (computation, section TI83), 1623
ME.TI86 (computation, section TI86), 1624
MEASM (subsection, section MO), 1625
MFLT (example), 1626
MI (definition), 1627
MI (example), 1628
MI (notation), 1629
MI.MMA (computation, section MMA), 1630
MI.SAGE (computation, section SAGE), 1631
MICN (Property), 1632
MIF (Property), 1633
MIMI (theorem), 1634
MINM (section), 1635
MISLE (section), 1636
MISM (theorem), 1637
MIT (theorem), 1638
MIU (theorem), 1639
MIVS (example), 1640
MLT (subsection, section LT), 1641
MLTCV (theorem), 1642
MLTLT (theorem), 1643
MM (definition), 1644
MM (section), 1645
MM (subsection, section MM), 1646
MM.MMA (computation, section MMA), 1647
MMA (section), 1648
MMA (theorem), 1649
MMAD (theorem), 1650
MMCC (theorem), 1651
MMDAA (theorem), 1652
MMEE (subsection, section MM), 1653
MMIM (theorem), 1654
MMIP (theorem), 1655
MMNC (example), 1656
MMSMM (theorem), 1657
MMT (theorem), 1658
MMZM (theorem), 1659
MNEM (theorem), 1660
MNSLE (example), 1661
MO (section), 1662
MOLT (example), 1663
more variables than equations
example OSGMD, 1664
theorem CMVEI, 1665
MPMR (example), 1666
MR (definition), 1667
MR (notation), 1668
MR (section), 1669
MRBE (example), 1670
MRCB (theorem), 1671
MRCLT (diagram), 1672
MRCLT (theorem), 1673
MRCM (example), 1674
MRLS (definition), 1675
MRLS (notation), 1676
MRMLT (theorem), 1677
MRRGE (theorem), 1678
MRS (subsection, section CB), 1679
MRSLT (theorem), 1680
MSCN (example), 1681
MSM (definition), 1682
MSM (example), 1683
MSM (notation), 1684
MTV (example), 1685
multiplicative associativity
complex numbers
Property MACN, 1686
multiplicative closure
complex numbers
Property MCCN, 1687
field
Property MCF, 1688
multiplicative commutativity
complex numbers
Property CMCN, 1689
multiplicative inverse
complex numbers
Property MICN, 1690
MVNSE (subsection, section RREF), 1691
MVP (definition), 1692
MVP (notation), 1693
MVP (subsection, section MM), 1694
MVSLD (theorem), 1695
MWIAA (example), 1696
N (archetype), 1697
N (subsection, section O), 1698
N (technique, section PT), 1699
NDMS4 (example), 1700
negation of statements
technique N, 1701
NEM (theorem), 1702
NI (theorem), 1703
NIAO (example), 1704
NIAQ (example), 1705
NIAQR (example), 1706
NIDAU (example), 1707
nilpotent
linear transformation
definition NLT, 1708
NILT (diagram), 1709
NJB (theorem), 1710
NJB5 (example), 1711
NKAO (example), 1712
NLT (definition), 1713
NLT (example), 1714
NLT (section), 1715
NLT (subsection, section NLT), 1716
NLTFO (subsection, section LT), 1717
NM (definition), 1718
NM (example), 1719
NM (section), 1720
NM (subsection, section NM), 1721
NM (subsection, section OD), 1722
NM62 (example), 1723
NM64 (example), 1724
NM83 (example), 1725
NME1 (theorem), 1726
NME2 (theorem), 1727
NME3 (theorem), 1728
NME4 (theorem), 1729
NME5 (theorem), 1730
NME6 (theorem), 1731
NME7 (theorem), 1732
NME8 (theorem), 1733
NME9 (theorem), 1734
NMI (subsection, section MINM), 1735
NMLIC (theorem), 1736
NMPEM (theorem), 1737
NMRRI (theorem), 1738
NMTNS (theorem), 1739
NMUS (theorem), 1740
NOILT (theorem), 1741
NOLT (definition), 1742
NOLT (notation), 1743
NOM (definition), 1744
NOM (notation), 1745
nonsingular
columns as basis
theorem CNMB, 1746
nonsingular matrices
linearly independent columns
theorem NMLIC, 1747
nonsingular matrix
Archetype B
example NM, 1748
column space, 1749
elementary matrices
theorem NMPEM, 1750
equivalences
theorem NME1, 1751
theorem NME2, 1752
theorem NME3, 1753
theorem NME4, 1754
theorem NME5, 1755
theorem NME6, 1756
theorem NME7, 1757
theorem NME8, 1758
theorem NME9, 1759
matrix inverse, 1760
null space
example NSNM, 1761
nullity, 1762
product of nonsingular matrices
theorem NPNT, 1763
rank
theorem RNNM, 1764
row-reduced
theorem NMRRI, 1765
trivial null space
theorem NMTNS, 1766
unique solutions
theorem NMUS, 1767
nonsingular matrix, row-reduced
example NSR, 1768
norm
example CNSV, 1769
inner product, 1770
notation, 1771
normal matrix
definition NRML, 1772
example ANM, 1773
orthonormal basis, 1774
notation
A, 1775
AM, 1776
AME, 1777
C, 1778
CCCV, 1779
CCM, 1780
CCN, 1781
CNA, 1782
CNE, 1783
CNM, 1784
CSM, 1785
CV, 1786
CVA, 1787
CVC, 1788
CVE, 1789
CVSM, 1790
D, 1791
DM, 1792
DS, 1793
ELEM, 1794
ES, 1795
GES, 1796
GME, 1797
HI, 1798
HID, 1799
HP, 1800
IE, 1801
IM, 1802
IP, 1803
JB, 1804
KLT, 1805
LNS, 1806
LT, 1807
LTR, 1808
M, 1809
MA, 1810
MC, 1811
ME, 1812
MI, 1813
MR, 1814
MRLS, 1815
MSM, 1816
MVP, 1817
NOLT, 1818
NOM, 1819
NSM, 1820
NV, 1821
RLT, 1822
RO, 1823
ROLT, 1824
ROM, 1825
RREFA, 1826
RSM, 1827
SC, 1828
SE, 1829
SETM, 1830
SI, 1831
SM, 1832
SRM, 1833
SSET, 1834
SSV, 1835
SU, 1836
SUV, 1837
T, 1838
TM, 1839
VR, 1840
VSCV, 1841
VSM, 1842
ZCV, 1843
ZM, 1844
notation for a linear system
example NSE, 1845
NPNT (theorem), 1846
NRFO (subsection, section MR), 1847
NRML (definition), 1848
NRREF (example), 1849
NS.MMA (computation, section MMA), 1850
NSAO (example), 1851
NSAQ (example), 1852
NSAQR (example), 1853
NSC2A (example), 1854
NSC2S (example), 1855
NSC2Z (example), 1856
NSDAT (example), 1857
NSDS (example), 1858
NSE (example), 1859
NSEAI (example), 1860
NSLE (example), 1861
NSLIL (example), 1862
NSM (definition), 1863
NSM (notation), 1864
NSM (subsection, section HSE), 1865
NSMS (theorem), 1866
NSNM (example), 1867
NSNM (subsection, section NM), 1868
NSR (example), 1869
NSS (example), 1870
NSSLI (subsection, section LI), 1871
Null space
as a span
example NSDS, 1872
null space
Archetype I
example NSEAI, 1873
basis
theorem BNS, 1874
computation
example CNS1, 1875
example CNS2, 1876
isomorphic to kernel, 1877
linearly independent basis
example LINSB, 1878
mathematica, 1879
matrix
definition NSM, 1880
nonsingular matrix, 1881
notation, 1882
singular matrix, 1883
spanning set
example SSNS, 1884
theorem SSNS, 1885
subspace
theorem NSMS, 1886
null space span, linearly independent
Archetype L
example NSLIL, 1887
nullity
computing, 1888
injective linear transformation
theorem NOILT, 1889
linear transformation
definition NOLT, 1890
matrix, 1891
definition NOM, 1892
notation, 1893, 1894
square matrix, 1895
NV (definition), 1896
NV (notation), 1897
NVM (theorem), 1898
O (archetype), 1899
O (Property), 1900
O (section), 1901
OBC (subsection, section B), 1902
OBNM (theorem), 1903
OBUTR (theorem), 1904
OC (Property), 1905
OCN (Property), 1906
OD (section), 1907
OD (subsection, section OD), 1908
OD (theorem), 1909
OF (Property), 1910
OLTTR (example), 1911
OM (Property), 1912
one
column vectors
Property OC, 1913
complex numbers
Property OCN, 1914
field
Property OF, 1915
matrices
Property OM, 1916
vectors
Property O, 1917
ONFV (example), 1918
ONS (definition), 1919
ONTV (example), 1920
orthogonal
linear independence
theorem OSLI, 1921
set
example AOS, 1922
set of vectors
definition OSV, 1923
vector pairs
definition OV, 1924
orthogonal vectors
example TOV, 1925
orthonormal
definition ONS, 1926
matrix columns
example OSMC, 1927
orthonormal basis
normal matrix
theorem OBNM, 1928
orthonormal diagonalization
theorem OD, 1929
orthonormal set
four vectors
example ONFV, 1930
three vectors
example ONTV, 1931
OSGMD (example), 1932
OSIS (theorem), 1933
OSLI (theorem), 1934
OSMC (example), 1935
OSV (definition), 1936
OV (definition), 1937
OV (subsection, section O), 1938
P (appendix), 1939
P (archetype), 1940
P (technique, section PT), 1941
particular solutions
example PSHS, 1942
PCNA (theorem), 1943
PCVS (example), 1944
PD (section), 1945
PDM (section), 1946
PDM (theorem), 1947
PEE (section), 1948
PEEF (theorem), 1949
PI (definition), 1950
PI (subsection, section LT), 1951
PI (technique, section PT), 1952
PIP (theorem), 1953
PM (example), 1954
PM (subsection, section EE), 1955
PMI (subsection, section MISLE), 1956
PMM (subsection, section MM), 1957
PMR (subsection, section MR), 1958
PNLT (subsection, section NLT), 1959
POD (section), 1960
polar decomposition
theorem PDM, 1961
polynomial
of a matrix
example PM, 1962
polynomial vector space
dimension
theorem DP, 1963
positive semi-definite
creating
theorem CPSM, 1964
positive semi-definite matrix
definition PSM, 1965
eigenvalues
theorem EPSM, 1966
practice
technique P, 1967
pre-image
definition PI, 1968
kernel
theorem KPI, 1969
pre-images
example SPIAS, 1970
principal axis theorem, 1971
product of triangular matrices
theorem PTMT, 1972
Property
AA, 1973
AAC, 1974
AACN, 1975
AAF, 1976
AAM, 1977
AC, 1978
ACC, 1979
ACCN, 1980
ACF, 1981
ACM, 1982
AI, 1983
AIC, 1984
AICN, 1985
AIF, 1986
AIM, 1987
C, 1988
CACN, 1989
CAF, 1990
CC, 1991
CM, 1992
CMCN, 1993
CMF, 1994
DCN, 1995
DF, 1996
DMAM, 1997
DSA, 1998
DSAC, 1999
DSAM, 2000
DVA, 2001
DVAC, 2002
MACN, 2003
MAF, 2004
MCCN, 2005
MCF, 2006
MICN, 2007
MIF, 2008
O, 2009
OC, 2010
OCN, 2011
OF, 2012
OM, 2013
SC, 2014
SCC, 2015
SCM, 2016
SMA, 2017
SMAC, 2018
SMAM, 2019
Z, 2020
ZC, 2021
ZCN, 2022
ZF, 2023
ZM, 2024
PSHS (example), 2025
PSHS (subsection, section LC), 2026
PSM (definition), 2027
PSM (section), 2028
PSM (subsection, section PSM), 2029
PSM (subsection, section SD), 2030
PSMSR (theorem), 2031
PSPHS (theorem), 2032
PSS (subsection, section SSLE), 2033
PSSD (theorem), 2034
PSSLS (theorem), 2035
PT (section), 2036
PTFP (example), 2037
PTM (example), 2038
PTMEE (example), 2039
PTMT (theorem), 2040
Q (archetype), 2041
R (acronyms, section JCF), 2042
R (archetype), 2043
R (chapter), 2044
R.SAGE (computation, section SAGE), 2045
range
full
example FRAN, 2046
isomorphic to column space
theorem RCSI, 2047
linear transformation
example RAO, 2048
notation, 2049
of a linear transformation
definition RLT, 2050
pre-image
theorem RPI, 2051
subspace
theorem RLTS, 2052
surjective linear transformation
theorem RSLT, 2053
via matrix representation
example RVMR, 2054
rank
computing
theorem CRN, 2055
linear transformation
definition ROLT, 2056
matrix
definition ROM, 2057
example RNM, 2058
notation, 2059, 2060
of transpose
example RRTI, 2061
square matrix
example RNSM, 2062
surjective linear transformation
theorem ROSLT, 2063
transpose
theorem RMRT, 2064
rank one decomposition
size 2
example ROD2, 2065
size 4
example ROD4, 2066
theorem ROD, 2067
rank+nullity
theorem RPNC, 2068
RAO (example), 2069
RCLS (theorem), 2070
RCSI (theorem), 2071
RD (subsection, section VS), 2072
RDS (theorem), 2073
READ (subsection, section B), 2074
READ (subsection, section CB), 2075
READ (subsection, section CRS), 2076
READ (subsection, section D), 2077
READ (subsection, section DM), 2078
READ (subsection, section EE), 2079
READ (subsection, section FS), 2080
READ (subsection, section HSE), 2081
READ (subsection, section ILT), 2082
READ (subsection, section IVLT), 2083
READ (subsection, section LC), 2084
READ (subsection, section LDS), 2085
READ (subsection, section LI), 2086
READ (subsection, section LISS), 2087
READ (subsection, section LT), 2088
READ (subsection, section MINM), 2089
READ (subsection, section MISLE), 2090
READ (subsection, section MM), 2091
READ (subsection, section MO), 2092
READ (subsection, section MR), 2093
READ (subsection, section NM), 2094
READ (subsection, section O), 2095
READ (subsection, section PD), 2096
READ (subsection, section PDM), 2097
READ (subsection, section PEE), 2098
READ (subsection, section RREF), 2099
READ (subsection, section S), 2100
READ (subsection, section SD), 2101
READ (subsection, section SLT), 2102
READ (subsection, section SS), 2103
READ (subsection, section SSLE), 2104
READ (subsection, section TSS), 2105
READ (subsection, section VO), 2106
READ (subsection, section VR), 2107
READ (subsection, section VS), 2108
READ (subsection, section WILA), 2109
reduced row-echelon form
analysis
notation, 2110
definition RREF, 2111
example NRREF, 2112
example RREF, 2113
extended
definition EEF, 2114
notation
example RREFN, 2115
unique
theorem RREFU, 2116
reducing a span
example RSC5, 2117
relation of linear dependence
definition RLD, 2118
definition RLDCV, 2119
REM (definition), 2120
REMEF (theorem), 2121
REMES (theorem), 2122
REMRS (theorem), 2123
RES (example), 2124
RGEN (theorem), 2125
rings
sage, 2126
RLD (definition), 2127
RLDCV (definition), 2128
RLT (definition), 2129
RLT (notation), 2130
RLT (subsection, section IS), 2131
RLT (subsection, section SLT), 2132
RLTS (theorem), 2133
RMRT (theorem), 2134
RNLT (subsection, section IVLT), 2135
RNM (example), 2136
RNM (subsection, section D), 2137
RNNM (subsection, section D), 2138
RNNM (theorem), 2139
RNSM (example), 2140
RO (definition), 2141
RO (notation), 2142
RO (subsection, section RREF), 2143
ROD (section), 2144
ROD (theorem), 2145
ROD2 (example), 2146
ROD4 (example), 2147
ROLT (definition), 2148
ROLT (notation), 2149
ROM (definition), 2150
ROM (notation), 2151
ROSLT (theorem), 2152
row operations
definition RO, 2153
elementary matrices, 2154, 2155
notation, 2156
row reduce
mathematica, 2157
sage, 2158
ti83, 2159
ti86, 2160
row space
Archetype I
example RSAI, 2161
as column space, 2162
basis
example RSB, 2163
theorem BRS, 2164
matrix, 2165
notation, 2166
row-equivalent matrices
theorem REMRS, 2167
subspace
theorem RSMS, 2168
row-equivalent matrices
definition REM, 2169
example TREM, 2170
row space, 2171
row spaces
example RSREM, 2172
theorem REMES, 2173
row-reduce
the verb
definition RR, 2174
row-reduced matrices
theorem REMEF, 2175
RPI (theorem), 2176
RPNC (theorem), 2177
RPNDD (theorem), 2178
RR (definition), 2179
RR.MMA (computation, section MMA), 2180
RR.SAGE (computation, section SAGE), 2181
RR.TI83 (computation, section TI83), 2182
RR.TI86 (computation, section TI86), 2183
RREF (definition), 2184
RREF (example), 2185
RREF (section), 2186
RREF (subsection, section RREF), 2187
RREFA (notation), 2188
RREFN (example), 2189
RREFU (theorem), 2190
RRTI (example), 2191
RS (example), 2192
RSAI (example), 2193
RSB (example), 2194
RSC4 (example), 2195
RSC5 (example), 2196
RSLT (theorem), 2197
RSM (definition), 2198
RSM (notation), 2199
RSM (subsection, section CRS), 2200
RSMS (theorem), 2201
RSNS (example), 2202
RSREM (example), 2203
RT (subsection, section PD), 2204
RVMR (example), 2205
S (archetype), 2206
S (definition), 2207
S (example), 2208
S (section), 2209
SAA (example), 2210
SAB (example), 2211
SABMI (example), 2212
SAE (example), 2213
sage
eigenspaces (computation), 2214
linear solve (computation), 2215
matrix entry (computation), 2216
matrix inverse (computation), 2217
rings (computation), 2218
row reduce (computation), 2219
transpose of a matrix (computation), 2220
vector linear combinations (computation), 2221
SAGE (section), 2222
SAN (example), 2223
SAR (example), 2224
SAS (section), 2225
SAV (example), 2226
SC (definition), 2227
SC (example), 2228
SC (notation), 2229
SC (Property), 2230
SC (subsection, section S), 2231
SC (subsection, section SET), 2232
SC3 (example), 2233
SCAA (example), 2234
SCAB (example), 2235
SCAD (example), 2236
scalar closure
column vectors
Property SCC, 2237
matrices
Property SCM, 2238
vectors
Property SC, 2239
scalar multiple
matrix inverse, 2240
scalar multiplication
zero scalar
theorem ZSSM, 2241
zero vector
theorem ZVSM, 2242
zero vector result
theorem SMEZV, 2243
scalar multiplication associativity
column vectors
Property SMAC, 2244
matrices
Property SMAM, 2245
vectors
Property SMA, 2246
SCB (theorem), 2247
SCC (Property), 2248
SCM (Property), 2249
SD (section), 2250
SDS (example), 2251
SE (definition), 2252
SE (notation), 2253
secret sharing
6 ways
example SS6W, 2254
SEE (example), 2255
SEEF (example), 2256
SER (theorem), 2257
set
cardinality
definition C, 2258
example CS, 2259
notation, 2260
complement
definition SC, 2261
example SC, 2262
notation, 2263
definition SET, 2264
empty
definition ES, 2265
equality
definition SE, 2266
notation, 2267
intersection
definition SI, 2268
example SI, 2269
notation, 2270
membership
example SETM, 2271
notation, 2272
size, 2273
subset, 2274
union
definition SU, 2275
example SU, 2276
notation, 2277
SET (definition), 2278
SET (section), 2279
SETM (example), 2280
SETM (notation), 2281
shoes, 2282
SHS (subsection, section HSE), 2283
SI (definition), 2284
SI (example), 2285
SI (notation), 2286
SI (subsection, section IVLT), 2287
SIM (definition), 2288
similar matrices
equal eigenvalues
example EENS, 2289
eual eigenvalues
theorem SMEE, 2290
example SMS3, 2291
example SMS5, 2292
similarity
definition SIM, 2293
equivalence relation
theorem SER, 2294
singular matrix
Archetype A
example S, 2295
null space
example NSS, 2296
singular matrix, row-reduced
example SRR, 2297
singular value decomposition
theorem SVD, 2298
singular values
definition SV, 2299
SLE (acronyms, section NM), 2300
SLE (chapter), 2301
SLE (definition), 2302
SLE (subsection, section SSLE), 2303
SLELT (subsection, section IVLT), 2304
SLEMM (theorem), 2305
SLSLC (theorem), 2306
SLT (definition), 2307
SLT (section), 2308
SLTB (theorem), 2309
SLTD (subsection, section SLT), 2310
SLTD (theorem), 2311
SLTLT (theorem), 2312
SM (definition), 2313
SM (notation), 2314
SM (subsection, section SD), 2315
SM2Z7 (example), 2316
SM32 (example), 2317
SMA (Property), 2318
SMAC (Property), 2319
SMAM (Property), 2320
SMEE (theorem), 2321
SMEZV (theorem), 2322
SMLT (example), 2323
SMS (theorem), 2324
SMS3 (example), 2325
SMS5 (example), 2326
SMZD (theorem), 2327
SMZE (theorem), 2328
SNCM (theorem), 2329
SO (subsection, section SET), 2330
socks, 2331
SOL (subsection, section B), 2332
SOL (subsection, section CB), 2333
SOL (subsection, section CRS), 2334
SOL (subsection, section D), 2335
SOL (subsection, section DM), 2336
SOL (subsection, section EE), 2337
SOL (subsection, section F), 2338
SOL (subsection, section FS), 2339
SOL (subsection, section HSE), 2340
SOL (subsection, section ILT), 2341
SOL (subsection, section IVLT), 2342
SOL (subsection, section LC), 2343
SOL (subsection, section LDS), 2344
SOL (subsection, section LI), 2345
SOL (subsection, section LISS), 2346
SOL (subsection, section LT), 2347
SOL (subsection, section MINM), 2348
SOL (subsection, section MISLE), 2349
SOL (subsection, section MM), 2350
SOL (subsection, section MO), 2351
SOL (subsection, section MR), 2352
SOL (subsection, section NM), 2353
SOL (subsection, section O), 2354
SOL (subsection, section PD), 2355
SOL (subsection, section PDM), 2356
SOL (subsection, section PEE), 2357
SOL (subsection, section RREF), 2358
SOL (subsection, section S), 2359
SOL (subsection, section SD), 2360
SOL (subsection, section SLT), 2361
SOL (subsection, section SS), 2362
SOL (subsection, section SSLE), 2363
SOL (subsection, section T), 2364
SOL (subsection, section TSS), 2365
SOL (subsection, section VO), 2366
SOL (subsection, section VR), 2367
SOL (subsection, section VS), 2368
SOL (subsection, section WILA), 2369
solution set
Archetype A
example SAA, 2370
archetype E
example SAE, 2371
theorem PSPHS, 2372
solution set of a linear system
definition SSSLE, 2373
solution sets
possibilities
theorem PSSLS, 2374
solution to a linear system
definition SSLE, 2375
solution vector
definition SOLV, 2376
SOLV (definition), 2377
solving homogeneous system
Archetype A
example HISAA, 2378
Archetype B
example HUSAB, 2379
Archetype D
example HISAD, 2380
solving nonlinear equations
example STNE, 2381
SP4 (example), 2382
span
basic
example ABS, 2383
basis
theorem BS, 2384
definition SS, 2385
definition SSCV, 2386
improved
example IAS, 2387
notation, 2388
reducing
example RSC4, 2389
reduction
example RS, 2390
removing vectors
example COV, 2391
reworking elements
example RES, 2392
set of polynomials
example SSP, 2393
subspace
theorem SSS, 2394
span of columns
Archetype A
example SCAA, 2395
Archetype B
example SCAB, 2396
Archetype D
example SCAD, 2397
spanning set
crazy vector space
example SSC, 2398
definition TSVS, 2399
matrices
example SSM22, 2400
more vectors
theorem SSLD, 2401
polynomials
example SSP4, 2402
SPIAS (example), 2403
SQM (definition), 2404
square root
eigenvalues, eigenspaces
theorem EESR, 2405
matrix
definition SRM, 2406
notation, 2407
positive semi-definite matrix
theorem PSMSR, 2408
unique
theorem USR, 2409
SR (section), 2410
SRM (definition), 2411
SRM (notation), 2412
SRM (subsection, section SR), 2413
SRR (example), 2414
SS (definition), 2415
SS (example), 2416
SS (section), 2417
SS (subsection, section LISS), 2418
SS (theorem), 2419
SS6W (example), 2420
SSC (example), 2421
SSCV (definition), 2422
SSET (definition), 2423
SSET (example), 2424
SSET (notation), 2425
SSLD (theorem), 2426
SSLE (definition), 2427
SSLE (section), 2428
SSM22 (example), 2429
SSNS (example), 2430
SSNS (subsection, section SS), 2431
SSNS (theorem), 2432
SSP (example), 2433
SSP4 (example), 2434
SSRLT (theorem), 2435
SSS (theorem), 2436
SSSLE (definition), 2437
SSSLT (subsection, section SLT), 2438
SSV (notation), 2439
SSV (subsection, section SS), 2440
standard unit vector
notation, 2441
starting proofs
technique GS, 2442
STLT (example), 2443
STNE (example), 2444
SU (definition), 2445
SU (example), 2446
SU (notation), 2447
submatrix
notation, 2448
subset
definition SSET, 2449
notation, 2450
subspace
as null space
example RSNS, 2451
characterized
example ASC, 2452
definition S, 2453
in {P}_{4}
example SP4, 2454
not, additive closure
example NSC2A, 2455
not, scalar closure
example NSC2S, 2456
not, zero vector
example NSC2Z, 2457
testing
theorem TSS, 2458
trivial
definition TS, 2459
verification
example SC3, 2460
example SM32, 2461
subspaces
equal dimension
theorem EDYES, 2462
surjective
Archetype N
example SAN, 2463
example SAR, 2464
not
example NSAQ, 2465
example NSAQR, 2466
not, Archetype O
example NSAO, 2467
not, by dimension
example NSDAT, 2468
polynomials to matrices
example SAV, 2469
surjective linear transformation
bases
theorem SLTB, 2470
surjective linear transformations
dimension
theorem SLTD, 2471
SUV (definition), 2472
SUV (notation), 2473
SUVB (theorem), 2474
SUVOS (example), 2475
SV (definition), 2476
SVD (section), 2477
SVD (subsection, section SVD), 2478
SVD (theorem), 2479
SVP4 (example), 2480
SYM (definition), 2481
SYM (example), 2482
symmetric matrices
theorem SMS, 2483
symmetric matrix
example SYM, 2484
system of equations
vector equality
example VESE, 2485
system of linear equations
definition SLE, 2486
T (archetype), 2487
T (definition), 2488
T (notation), 2489
T (part), 2490
T (section), 2491
T (technique, section PT), 2492
TCSD (example), 2493
TD (section), 2494
TD (subsection, section TD), 2495
TD (theorem), 2496
TD4 (example), 2497
TDEE (theorem), 2498
TDEE6 (example), 2499
TDSSE (example), 2500
TDSSE (subsection, section TD), 2501
technique
C, 2502
CD, 2503
CP, 2504
CV, 2505
D, 2506
DC, 2507
E, 2508
GS, 2509
I, 2510
L, 2511
LC, 2512
ME, 2513
N, 2514
P, 2515
PI, 2516
T, 2517
U, 2518
theorem
AA, 2519
AIP, 2520
AISM, 2521
AIU, 2522
AMA, 2523
AMSM, 2524
BCS, 2525
BIS, 2526
BNS, 2527
BRS, 2528
BS, 2529
CB, 2530
CCM, 2531
CCRA, 2532
CCRM, 2533
CCT, 2534
CFDVS, 2535
CFNLT, 2536
CHT, 2537
CILTI, 2538
CINM, 2539
CIVLT, 2540
CLI, 2541
CLTLT, 2542
CMVEI, 2543
CNMB, 2544
COB, 2545
CPSM, 2546
CRMA, 2547
CRMSM, 2548
CRN, 2549
CRSM, 2550
CRVA, 2551
CSCS, 2552
CSLTS, 2553
CSMS, 2554
CSNM, 2555
CSRN, 2556
CSRST, 2557
CSS, 2558
CUMOS, 2559
DC, 2560
DCM, 2561
DCP, 2562
DEC, 2563
DED, 2564
DEM, 2565
DEMMM, 2566
DER, 2567
DERC, 2568
DFS, 2569
DGES, 2570
DIM, 2571
DLDS, 2572
DM, 2573
DMFE, 2574
DMHP, 2575
DMMP, 2576
DMST, 2577
DNLT, 2578
DP, 2579
DRCM, 2580
DRCMA, 2581
DRCS, 2582
DRMM, 2583
DSD, 2584
DSFB, 2585
DSFOS, 2586
DSLI, 2587
DSZI, 2588
DSZV, 2589
DT, 2590
DVM, 2591
DZRC, 2592
EDELI, 2593
EDYES, 2594
EEMAP, 2595
EER, 2596
EESR, 2597
EIM, 2598
EIS, 2599
ELIS, 2600
EMDRO, 2601
EMHE, 2602
EMMVP, 2603
EMN, 2604
EMNS, 2605
EMP, 2606
EMRCP, 2607
EMS, 2608
ENLT, 2609
EOMP, 2610
EOPSS, 2611
EPM, 2612
EPSM, 2613
ERMCP, 2614
ESMM, 2615
ETM, 2616
FIMP, 2617
FS, 2618
FTMR, 2619
FVCS, 2620
G, 2621
GEK, 2622
GESD, 2623
GESIS, 2624
GSP, 2625
HMIP, 2626
HMOE, 2627
HMRE, 2628
HMVEI, 2629
HPC, 2630
HPDAA, 2631
HPHI, 2632
HPHID, 2633
HPSMM, 2634
HSC, 2635
ICBM, 2636
ICLT, 2637
IFDVS, 2638
IILT, 2639
ILTB, 2640
ILTD, 2641
ILTIS, 2642
ILTLI, 2643
ILTLT, 2644
IMILT, 2645
IMR, 2646
IP, 2647
IPAC, 2648
IPN, 2649
IPSM, 2650
IPVA, 2651
ISRN, 2652
ITMT, 2653
IVSED, 2654
JCFLT, 2655
KILT, 2656
KLTS, 2657
KNSI, 2658
KPI, 2659
KPIS, 2660
KPLT, 2661
KPNLT, 2662
LIVHS, 2663
LIVRN, 2664
LNSMS, 2665
LSMR, 2666
LTDB, 2667
LTLC, 2668
LTTZZ, 2669
MBLT, 2670
MCT, 2671
ME, 2672
MIMI, 2673
MISM, 2674
MIT, 2675
MIU, 2676
MLTCV, 2677
MLTLT, 2678
MMA, 2679
MMAD, 2680
MMCC, 2681
MMDAA, 2682
MMIM, 2683
MMIP, 2684
MMSMM, 2685
MMT, 2686
MMZM, 2687
MNEM, 2688
MRCB, 2689
MRCLT, 2690
MRMLT, 2691
MRRGE, 2692
MRSLT, 2693
MVSLD, 2694
NEM, 2695
NI, 2696
NJB, 2697
NME1, 2698
NME2, 2699
NME3, 2700
NME4, 2701
NME5, 2702
NME6, 2703
NME7, 2704
NME8, 2705
NME9, 2706
NMLIC, 2707
NMPEM, 2708
NMRRI, 2709
NMTNS, 2710
NMUS, 2711
NOILT, 2712
NPNT, 2713
NSMS, 2714
NVM, 2715
OBNM, 2716
OBUTR, 2717
OD, 2718
OSIS, 2719
OSLI, 2720
PCNA, 2721
PDM, 2722
PEEF, 2723
PIP, 2724
PSMSR, 2725
PSPHS, 2726
PSSD, 2727
PSSLS, 2728
PTMT, 2729
RCLS, 2730
RCSI, 2731
RDS, 2732
REMEF, 2733
REMES, 2734
REMRS, 2735
RGEN, 2736
RLTS, 2737
RMRT, 2738
RNNM, 2739
ROD, 2740
ROSLT, 2741
RPI, 2742
RPNC, 2743
RPNDD, 2744
RREFU, 2745
RSLT, 2746
RSMS, 2747
SCB, 2748
SER, 2749
SLEMM, 2750
SLSLC, 2751
SLTB, 2752
SLTD, 2753
SLTLT, 2754
SMEE, 2755
SMEZV, 2756
SMS, 2757
SMZD, 2758
SMZE, 2759
SNCM, 2760
SS, 2761
SSLD, 2762
SSNS, 2763
SSRLT, 2764
SSS, 2765
SUVB, 2766
SVD, 2767
TD, 2768
TDEE, 2769
technique T, 2770
TIST, 2771
TL, 2772
TMA, 2773
TMSM, 2774
TSE, 2775
TSRM, 2776
TSS, 2777
TT, 2778
TTMI, 2779
UMCOB, 2780
UMI, 2781
UMPIP, 2782
USR, 2783
UTMR, 2784
VFSLS, 2785
VRI, 2786
VRILT, 2787
VRLT, 2788
VRRB, 2789
VRS, 2790
VSLT, 2791
VSPCV, 2792
VSPM, 2793
ZSSM, 2794
ZVSM, 2795
ZVU, 2796
ti83
matrix entry (computation), 2797
row reduce (computation), 2798
vector linear combinations (computation), 2799
TI83 (section), 2800
ti86
matrix entry (computation), 2801
row reduce (computation), 2802
transpose of a matrix (computation), 2803
vector linear combinations (computation), 2804
TI86 (section), 2805
TIS (example), 2806
TIST (theorem), 2807
TIVS (example), 2808
TKAP (example), 2809
TL (theorem), 2810
TLC (example), 2811
TM (definition), 2812
TM (example), 2813
TM (notation), 2814
TM (subsection, section OD), 2815
TM.MMA (computation, section MMA), 2816
TM.SAGE (computation, section SAGE), 2817
TM.TI86 (computation, section TI86), 2818
TMA (theorem), 2819
TMP (example), 2820
TMSM (theorem), 2821
TOV (example), 2822
trace
definition T, 2823
linearity
theorem TL, 2824
matrix multiplication
theorem TSRM, 2825
notation, 2826
similarity
theorem TIST, 2827
sum of eigenvalues
theorem TSE, 2828
trail mix
example TMP, 2829
transpose
matrix scalar multiplication
theorem TMSM, 2830
example TM, 2831
matrix addition
theorem TMA, 2832
matrix inverse, 2833, 2834
notation, 2835
scalar multiplication, 2836
transpose of a matrix
mathematica, 2837
sage, 2838
ti86, 2839
transpose of a transpose
theorem TT, 2840
TREM (example), 2841
triangular decomposition
entry by entry, size 6
example TDEE6, 2842
entry by entry
theorem TDEE, 2843
size 4
example TD4, 2844
solving systems of equations
example TDSSE, 2845
theorem TD, 2846
triangular matrix
inverse
theorem ITMT, 2847
trivial solution
system of equations
definition TSHSE, 2848
TS (definition), 2849
TS (subsection, section S), 2850
TSE (theorem), 2851
TSHSE (definition), 2852
TSM (subsection, section MO), 2853
TSRM (theorem), 2854
TSS (section), 2855
TSS (subsection, section S), 2856
TSS (theorem), 2857
TSVS (definition), 2858
TT (theorem), 2859
TTMI (theorem), 2860
TTS (example), 2861
typical systems, 2 × 2
example TTS, 2862
U (archetype), 2863
U (technique, section PT), 2864
UM (definition), 2865
UM (subsection, section MINM), 2866
UM3 (example), 2867
UMCOB (theorem), 2868
UMI (theorem), 2869
UMPIP (theorem), 2870
unique solution, 3 × 3
example US, 2871
example USR, 2872
uniqueness
technique U, 2873
unit vectors
basis
theorem SUVB, 2874
definition SUV, 2875
orthogonal
example SUVOS, 2876
unitary
permutation matrix
example UPM, 2877
size 3
example UM3, 2878
unitary matrices
columns
theorem CUMOS, 2879
unitary matrix
inner product
theorem UMPIP, 2880
UPM (example), 2881
upper triangular matrix
definition UTM, 2882
US (example), 2883
USR (example), 2884
USR (theorem), 2885
UTM (definition), 2886
UTMR (subsection, section OD), 2887
UTMR (theorem), 2888
V (acronyms, section O), 2889
V (archetype), 2890
V (chapter), 2891
VA (example), 2892
Vandermonde matrix
definition VM, 2893
vandermonde matrix
determinant
theorem DVM, 2894
nonsingular
theorem NVM, 2895
size 4
example VM4, 2896
VEASM (subsection, section VO), 2897
vector
addition
definition CVA, 2898
column
definition CV, 2899
equality
definition CVE, 2900
notation, 2901
inner product
definition IP, 2902
norm
definition NV, 2903
notation, 2904
of constants
definition VOC, 2905
product with matrix, 2906, 2907
scalar multiplication
definition CVSM, 2908
vector addition
example VA, 2909
vector component
notation, 2910
vector form of solutions
Archetype D
example VFSAD, 2911
Archetype I
example VFSAI, 2912
Archetype L
example VFSAL, 2913
example VFS, 2914
mathematica, 2915
theorem VFSLS, 2916
vector linear combinations
mathematica, 2917
sage, 2918
ti83, 2919
ti86, 2920
vector representation
example AVR, 2921
example VRC4, 2922
injective
theorem VRI, 2923
invertible
theorem VRILT, 2924
linear transformation
definition VR, 2925
notation, 2926
theorem VRLT, 2927
surjective
theorem VRS, 2928
theorem VRRB, 2929
vector representations
polynomials
example VRP2, 2930
vector scalar multiplication
example CVSM, 2931
vector space
characterization
theorem CFDVS, 2932
column vectors
definition VSCV, 2933
definition VS, 2934
infinite dimension
example VSPUD, 2935
linear transformations
theorem VSLT, 2936
over integers mod 5
example VSIM5, 2937
vector space of column vectors
notation, 2938
vector space of functions
example VSF, 2939
vector space of infinite sequences
example VSIS, 2940
vector space of matrices
definition VSM, 2941
example VSM, 2942
notation, 2943
vector space of polynomials
example VSP, 2944
vector space properties
column vectors
theorem VSPCV, 2945
matrices
theorem VSPM, 2946
vector space, crazy
example CVS, 2947
vector space, singleton
example VSS, 2948
vector spaces
isomorphic
definition IVS, 2949
theorem IFDVS, 2950
VESE (example), 2951
VFS (example), 2952
VFSAD (example), 2953
VFSAI (example), 2954
VFSAL (example), 2955
VFSLS (theorem), 2956
VFSS (subsection, section LC), 2957
VFSS.MMA (computation, section MMA), 2958
VLC.MMA (computation, section MMA), 2959
VLC.SAGE (computation, section SAGE), 2960
VLC.TI83 (computation, section TI83), 2961
VLC.TI86 (computation, section TI86), 2962
VM (definition), 2963
VM (section), 2964
VM4 (example), 2965
VO (section), 2966
VOC (definition), 2967
VR (definition), 2968
VR (notation), 2969
VR (section), 2970
VR (subsection, section LISS), 2971
VRC4 (example), 2972
VRI (theorem), 2973
VRILT (theorem), 2974
VRLT (theorem), 2975
VRP2 (example), 2976
VRRB (theorem), 2977
VRS (theorem), 2978
VS (acronyms, section PD), 2979
VS (chapter), 2980
VS (definition), 2981
VS (section), 2982
VS (subsection, section VS), 2983
VSCV (definition), 2984
VSCV (example), 2985
VSCV (notation), 2986
VSF (example), 2987
VSIM5 (example), 2988
VSIS (example), 2989
VSLT (theorem), 2990
VSM (definition), 2991
VSM (example), 2992
VSM (notation), 2993
VSP (example), 2994
VSP (subsection, section MO), 2995
VSP (subsection, section VO), 2996
VSP (subsection, section VS), 2997
VSPCV (theorem), 2998
VSPM (theorem), 2999
VSPUD (example), 3000
VSS (example), 3001
W (archetype), 3002
WILA (section), 3003
X (archetype), 3004
Z (Property), 3005
ZC (Property), 3006
ZCN (Property), 3007
ZCV (definition), 3008
ZCV (notation), 3009
zero
complex numbers
Property ZCN, 3010
field
Property ZF, 3011
zero column vector
definition ZCV, 3012
notation, 3013
zero matrix
notation, 3014
zero vector
column vectors
Property ZC, 3015
matrices
Property ZM, 3016
unique
theorem ZVU, 3017
vectors
Property Z, 3018
ZF (Property), 3019
ZM (definition), 3020
ZM (notation), 3021
ZM (Property), 3022
ZNDAB (example), 3023
ZSSM (theorem), 3024
ZVSM (theorem), 3025
ZVU (theorem), 3026