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