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
RSC5, 952
RSNS, 953
RSREM, 954
RSSC4, 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 IVLT), 1044
EXC (subsection, section LC), 1045
EXC (subsection, section LDS), 1046
EXC (subsection, section LI), 1047
EXC (subsection, section LISS), 1048
EXC (subsection, section LT), 1049
EXC (subsection, section MINM), 1050
EXC (subsection, section MISLE), 1051
EXC (subsection, section MM), 1052
EXC (subsection, section MO), 1053
EXC (subsection, section MR), 1054
EXC (subsection, section NM), 1055
EXC (subsection, section O), 1056
EXC (subsection, section PD), 1057
EXC (subsection, section PDM), 1058
EXC (subsection, section PEE), 1059
EXC (subsection, section PSM), 1060
EXC (subsection, section RREF), 1061
EXC (subsection, section S), 1062
EXC (subsection, section SD), 1063
EXC (subsection, section SLT), 1064
EXC (subsection, section SS), 1065
EXC (subsection, section SSLE), 1066
EXC (subsection, section T), 1067
EXC (subsection, section TSS), 1068
EXC (subsection, section VO), 1069
EXC (subsection, section VR), 1070
EXC (subsection, section VS), 1071
EXC (subsection, section WILA), 1072
extended echelon form
submatrices
example SEEF, 1073
extended reduced row-echelon form
properties
theorem PEEF, 1074
F (archetype), 1075
F (definition), 1076
F (section), 1077
F (subsection, section F), 1078
FDV (example), 1079
FF (subsection, section F), 1080
FF8 (example), 1081
Fibonacci sequence
example FSCF, 1082
field
definition F, 1083
FIMP (theorem), 1084
finite field
size 8
example FF8, 1085
four subsets
example FS1, 1086
example FS2, 1087
four subspaces
dimension
theorem DFS, 1088
FRAN (example), 1089
free variables
example CFV, 1090
free variables, number
theorem FVCS, 1091
free, independent variables
example FDV, 1092
FS (section), 1093
FS (subsection, section FS), 1094
FS (subsection, section SD), 1095
FS (theorem), 1096
FS1 (example), 1097
FS2 (example), 1098
FSAG (example), 1099
FSCF (example), 1100
FTMR (diagram), 1101
FTMR (theorem), 1102
FTMRA (diagram), 1103
FV (subsection, section TSS), 1104
FVCS (theorem), 1105
G (archetype), 1106
G (theorem), 1107
GE4 (example), 1108
GE6 (example), 1109
GEE (subsection, section IS), 1110
GEK (theorem), 1111
generalized eigenspace
as kernel
theorem GEK, 1112
definition GES, 1113
dimension
theorem DGES, 1114
dimension 4 domain
example GE4, 1115
dimension 6 domain
example GE6, 1116
invariant subspace
theorem GESIS, 1117
nilpotent restriction
theorem RGEN, 1118
nilpotent restrictions, dimension 6 domain
example GENR6, 1119
notation, 1120
generalized eigenspace decomposition
theorem GESD, 1121
generalized eigenvector
definition GEV, 1122
GENR6 (example), 1123
GES (definition), 1124
GES (notation), 1125
GESD (subsection, section JCF), 1126
GESD (theorem), 1127
GESIS (theorem), 1128
GEV (definition), 1129
GFDL (appendix), 1130
GLT (diagram), 1131
GME (definition), 1132
GME (notation), 1133
goldilocks
theorem G, 1134
Gram-Schmidt
column vectors
theorem GSP, 1135
three vectors
example GSTV, 1136
gram-schmidt
mathematica, 1137
GS (technique, section PT), 1138
GSP (subsection, section O), 1139
GSP (theorem), 1140
GSP.MMA (computation, section MMA), 1141
GSTV (example), 1142
GT (subsection, section PD), 1143
H (archetype), 1144
Hadamard Identity
notation, 1145
Hadamard identity
definition HID, 1146
Hadamard Inverse
notation, 1147
Hadamard inverse
definition HI, 1148
Hadamard Product
Diagonalizable Matrices
theorem DMHP, 1149
notation, 1150
Hadamard product
commutativity
theorem HPC, 1151
definition HP, 1152
diagonal matrices
theorem DMMP, 1153
distributivity
theorem HPDAA, 1154
example HP, 1155
identity
theorem HPHID, 1156
inverse
theorem HPHI, 1157
scalar matrix multiplication
theorem HPSMM, 1158
hermitian
definition HM, 1159
Hermitian matrix
inner product
theorem HMIP, 1160
HI (definition), 1161
HI (notation), 1162
HID (definition), 1163
HID (notation), 1164
HISAA (example), 1165
HISAD (example), 1166
HM (definition), 1167
HM (subsection, section MM), 1168
HMEM5 (example), 1169
HMIP (theorem), 1170
HMOE (theorem), 1171
HMRE (theorem), 1172
HMVEI (theorem), 1173
homogeneous system
consistent
theorem HSC, 1174
definition HS, 1175
infinitely many solutions
theorem HMVEI, 1176
homogeneous systems
linear independence, 1177
homogenous system
Archetype C
example AHSAC, 1178
HP (definition), 1179
HP (example), 1180
HP (notation), 1181
HP (section), 1182
HPC (theorem), 1183
HPDAA (theorem), 1184
HPDM (example), 1185
HPHI (theorem), 1186
HPHID (theorem), 1187
HPSMM (theorem), 1188
HS (definition), 1189
HSC (theorem), 1190
HSE (section), 1191
HUSAB (example), 1192
I (archetype), 1193
I (technique, section PT), 1194
IAP (example), 1195
IAR (example), 1196
IAS (example), 1197
IAV (example), 1198
ICBM (theorem), 1199
ICLT (theorem), 1200
identities
technique PI, 1201
identity matrix
determinant, 1202
example IM, 1203
notation, 1204
IDLT (definition), 1205
IDV (definition), 1206
IE (definition), 1207
IE (notation), 1208
IFDVS (theorem), 1209
IILT (theorem), 1210
ILT (definition), 1211
ILT (diagram), 1212
ILT (section), 1213
ILTB (theorem), 1214
ILTD (subsection, section ILT), 1215
ILTD (theorem), 1216
ILTIS (theorem), 1217
ILTLI (subsection, section ILT), 1218
ILTLI (theorem), 1219
ILTLT (theorem), 1220
ILTVR (example), 1221
IM (definition), 1222
IM (example), 1223
IM (notation), 1224
IM (subsection, section MISLE), 1225
IM11 (example), 1226
IMILT (theorem), 1227
IMP (definition), 1228
IMR (theorem), 1229
inconsistent linear systems
theorem ISRN, 1230
independent, dependent variables
definition IDV, 1231
indesxstring
example SM2Z7, 1232
example SSET, 1233
index
eigenvalue
definition IE, 1234
notation, 1235
indexstring
theorem DRCMA, 1236
theorem OBUTR, 1237
theorem UMCOB, 1238
induction
technique I, 1239
infinite solution set
example ISSI, 1240
infinite solutions, 3 × 4
example IS, 1241
injective
example IAP, 1242
example IAR, 1243
not
example NIAO, 1244
example NIAQ, 1245
example NIAQR, 1246
not, by dimension
example NIDAU, 1247
polynomials to matrices
example IAV, 1248
injective linear transformation
bases
theorem ILTB, 1249
injective linear transformations
dimension
theorem ILTD, 1250
inner product
anti-commutative
theorem IPAC, 1251
example CSIP, 1252
norm
theorem IPN, 1253
notation, 1254
positive
theorem PIP, 1255
scalar multiplication
theorem IPSM, 1256
vector addition
theorem IPVA, 1257
integers
mod p
definition IMP, 1258
mod p, field
theorem FIMP, 1259
mod 11
example IM11, 1260
interpolating polynomial
theorem IP, 1261
invariant subspace
definition IS, 1262
eigenspace, 1263
eigenspaces
example EIS, 1264
example TIS, 1265
Jordan block
example ISJB, 1266
kernels of powers
theorem KPIS, 1267
inverse
composition of linear transformations
theorem ICLT, 1268
example CMI, 1269
example MI, 1270
notation, 1271
of a matrix, 1272
invertible linear transformation
defined by invertible matrix
theorem IMILT, 1273
invertible linear transformations
composition
theorem CIVLT, 1274
computing
example CIVLT, 1275
IP (definition), 1276
IP (notation), 1277
IP (subsection, section O), 1278
IP (theorem), 1279
IPAC (theorem), 1280
IPN (theorem), 1281
IPSM (theorem), 1282
IPVA (theorem), 1283
IS (definition), 1284
IS (example), 1285
IS (section), 1286
IS (subsection, section IS), 1287
ISJB (example), 1288
ISMR4 (example), 1289
ISMR6 (example), 1290
isomorphic
multiple vector spaces
example MIVS, 1291
vector spaces
example IVSAV, 1292
isomorphic vector spaces
dimension
theorem IVSED, 1293
example TIVS, 1294
ISRN (theorem), 1295
ISSI (example), 1296
ITMT (theorem), 1297
IV (subsection, section IVLT), 1298
IVLT (definition), 1299
IVLT (section), 1300
IVLT (subsection, section IVLT), 1301
IVLT (subsection, section MR), 1302
IVS (definition), 1303
IVSAV (example), 1304
IVSED (theorem), 1305
J (archetype), 1306
JB (definition), 1307
JB (notation), 1308
JB4 (example), 1309
JCF (definition), 1310
JCF (section), 1311
JCF (subsection, section JCF), 1312
JCF10 (example), 1313
JCFLT (theorem), 1314
Jordan block
definition JB, 1315
nilpotent
theorem NJB, 1316
notation, 1317
size 4
example JB4, 1318
Jordan canonical form
definition JCF, 1319
size 10
example JCF10, 1320
K (archetype), 1321
kernel
injective linear transformation
theorem KILT, 1322
isomorphic to null space
theorem KNSI, 1323
linear transformation
example NKAO, 1324
notation, 1325
of a linear transformation
definition KLT, 1326
pre-image, 1327
subspace
theorem KLTS, 1328
trivial
example TKAP, 1329
via matrix representation
example KVMR, 1330
KILT (theorem), 1331
KLT (definition), 1332
KLT (notation), 1333
KLT (subsection, section ILT), 1334
KLTS (theorem), 1335
KNSI (theorem), 1336
KPI (theorem), 1337
KPIS (theorem), 1338
KPLT (theorem), 1339
KPNLT (example), 1340
KPNLT (theorem), 1341
KVMR (example), 1342
L (archetype), 1343
L (technique, section PT), 1344
LA (subsection, section WILA), 1345
LC (definition), 1346
LC (section), 1347
LC (subsection, section LC), 1348
LC (technique, section PT), 1349
LCCV (definition), 1350
LCM (example), 1351
LDCAA (example), 1352
LDHS (example), 1353
LDP4 (example), 1354
LDRN (example), 1355
LDS (example), 1356
LDS (section), 1357
LDSS (subsection, section LDS), 1358
least squares
minimizes residuals
theorem LSMR, 1359
least squares solution
definition LSS, 1360
left null space
as row space, 1361
definition LNS, 1362
example LNS, 1363
notation, 1364
subspace
theorem LNSMS, 1365
lemma
technique LC, 1366
LI (definition), 1367
LI (section), 1368
LI (subsection, section LISS), 1369
LIC (example), 1370
LICAB (example), 1371
LICV (definition), 1372
LIHS (example), 1373
LIM32 (example), 1374
linear combination
system of equations
example ABLC, 1375
definition LC, 1376
definition LCCV, 1377
example TLC, 1378
linear transformation, 1379
matrices
example LCM, 1380
system of equations
example AALC, 1381
linear combinations
solutions to linear systems
theorem SLSLC, 1382
linear dependence
more vectors than size
theorem MVSLD, 1383
linear independence
definition LI, 1384
definition LICV, 1385
homogeneous systems
theorem LIVHS, 1386
injective linear transformation
theorem ILTLI, 1387
matrices
example LIM32, 1388
orthogonal, 1389
r and n
theorem LIVRN, 1390
linear solve
mathematica, 1391
linear system
consistent
theorem RCLS, 1392
matrix representation
definition MRLS, 1393
notation, 1394
linear systems
notation
example MNSLE, 1395
example NSLE, 1396
linear transformation
polynomials to polynomials
example LTPP, 1397
addition
definition LTA, 1398
theorem MLTLT, 1399
theorem SLTLT, 1400
as matrix multiplication
example ALTMM, 1401
basis of range
example BRLT, 1402
checking
example ALT, 1403
composition
definition LTC, 1404
theorem CLTLT, 1405
defined by a matrix
example LTM, 1406
defined on a basis
example LTDB1, 1407
example LTDB2, 1408
example LTDB3, 1409
theorem LTDB, 1410
definition LT, 1411
identity
definition IDLT, 1412
injection
definition ILT, 1413
inverse
theorem ILTLT, 1414
inverse of inverse
theorem IILT, 1415
invertible
definition IVLT, 1416
example AIVLT, 1417
invertible, injective and surjective
theorem ILTIS, 1418
Jordan canonical form
theorem JCFLT, 1419
kernels of powers
theorem KPLT, 1420
linear combination
theorem LTLC, 1421
matrix of, 1422
example MFLT, 1423
example MOLT, 1424
not
example NLT, 1425
not invertible
example ANILT, 1426
notation, 1427
polynomials to matrices
example LTPM, 1428
rank plus nullity
theorem RPNDD, 1429
restriction
definition LTR, 1430
notation, 1431
scalar multiple
example SMLT, 1432
scalar multiplication
definition LTSM, 1433
spanning range
theorem SSRLT, 1434
sum
example STLT, 1435
surjection
definition SLT, 1436
vector space of, 1437
zero vector
theorem LTTZZ, 1438
linear transformation inverse
via matrix representation
example ILTVR, 1439
linear transformation restriction
on generalized eigenspace
example LTRGE, 1440
linear transformations
compositions
example CTLT, 1441
from matrices
theorem MBLT, 1442
linearly dependent
r < n
example LDRN, 1443
via homogeneous system
example LDHS, 1444
linearly dependent columns
Archetype A
example LDCAA, 1445
linearly dependent set
example LDS, 1446
linear combinations within
theorem DLDS, 1447
polynomials
example LDP4, 1448
linearly independent
crazy vector space
example LIC, 1449
extending sets
theorem ELIS, 1450
polynomials
example LIP4, 1451
via homogeneous system
example LIHS, 1452
linearly independent columns
Archetype B
example LICAB, 1453
linearly independent set
example LIS, 1454
example LLDS, 1455
LINM (subsection, section LI), 1456
LINSB (example), 1457
LIP4 (example), 1458
LIS (example), 1459
LISS (section), 1460
LISV (subsection, section LI), 1461
LIVHS (theorem), 1462
LIVRN (theorem), 1463
LLDS (example), 1464
LNS (definition), 1465
LNS (example), 1466
LNS (notation), 1467
LNS (subsection, section FS), 1468
LNSMS (theorem), 1469
lower triangular matrix
definition LTM, 1470
LS.MMA (computation, section MMA), 1471
LSMR (theorem), 1472
LSS (definition), 1473
LT (acronyms, section IVLT), 1474
LT (chapter), 1475
LT (definition), 1476
LT (notation), 1477
LT (section), 1478
LT (subsection, section LT), 1479
LTA (definition), 1480
LTC (definition), 1481
LTC (subsection, section LT), 1482
LTDB (theorem), 1483
LTDB1 (example), 1484
LTDB2 (example), 1485
LTDB3 (example), 1486
LTLC (subsection, section LT), 1487
LTLC (theorem), 1488
LTM (definition), 1489
LTM (example), 1490
LTPM (example), 1491
LTPP (example), 1492
LTR (definition), 1493
LTR (notation), 1494
LTRGE (example), 1495
LTSM (definition), 1496
LTTZZ (theorem), 1497
M (acronyms, section FS), 1498
M (archetype), 1499
M (chapter), 1500
M (definition), 1501
M (notation), 1502
MA (definition), 1503
MA (example), 1504
MA (notation), 1505
MACN (Property), 1506
MAF (Property), 1507
MAP (subsection, section SVD), 1508
mathematica
gram-schmidt (computation), 1509
linear solve (computation), 1510
matrix entry (computation), 1511
matrix inverse (computation), 1512
matrix multiplication (computation), 1513
null space (computation), 1514
row reduce (computation), 1515
transpose of a matrix (computation), 1516
vector form of solutions (computation), 1517
vector linear combinations (computation), 1518
mathematical language
technique L, 1519
matrix
addition
definition MA, 1520
notation, 1521
augmented
definition AM, 1522
column space
definition CSM, 1523
complex conjugate
example CCM, 1524
definition M, 1525
equality
definition ME, 1526
notation, 1527
example AM, 1528
identity
definition IM, 1529
inverse
definition MI, 1530
nonsingular
definition NM, 1531
notation, 1532
of a linear transformation
theorem MLTCV, 1533
product
example PTM, 1534
example PTMEE, 1535
product with vector
definition MVP, 1536
rectangular, 1537
row space
definition RSM, 1538
scalar multiplication
definition MSM, 1539
notation, 1540
singular, 1541
square
definition SQM, 1542
submatrices
example SS, 1543
submatrix
definition SM, 1544
symmetric
definition SYM, 1545
transpose
definition TM, 1546
unitary
definition UM, 1547
unitary is invertible
theorem UMI, 1548
zero
definition ZM, 1549
matrix addition
example MA, 1550
matrix components
notation, 1551
matrix entry
mathematica, 1552
sage, 1553
ti83, 1554
ti86, 1555
matrix inverse
Archetype B, 1556
computation
theorem CINM, 1557
mathematica, 1558
nonsingular matrix
theorem NI, 1559
of a matrix inverse
theorem MIMI, 1560
one-sided
theorem OSIS, 1561
product
theorem SS, 1562
sage, 1563
scalar multiple
theorem MISM, 1564
size 2 matrices
theorem TTMI, 1565
transpose
theorem MIT, 1566
uniqueness
theorem MIU, 1567
matrix multiplication
adjoints
theorem MMAD, 1568
associativity
theorem MMA, 1569
complex conjugation
theorem MMCC, 1570
definition MM, 1571
distributivity
theorem MMDAA, 1572
entry-by-entry
theorem EMP, 1573
identity matrix
theorem MMIM, 1574
inner product
theorem MMIP, 1575
mathematica, 1576
noncommutative
example MMNC, 1577
scalar matrix multiplication
theorem MMSMM, 1578
systems of linear equations
theorem SLEMM, 1579
transposes
theorem MMT, 1580
zero matrix
theorem MMZM, 1581
matrix product
as composition of linear transformations
example MPMR, 1582
matrix representation
basis of eigenvectors
example MRBE, 1583
composition of linear transformations
theorem MRCLT, 1584
definition MR, 1585
invertible
theorem IMR, 1586
multiple of a linear transformation
theorem MRMLT, 1587
notation, 1588
restriction to generalized eigenspace
theorem MRRGE, 1589
sum of linear transformations
theorem MRSLT, 1590
theorem FTMR, 1591
upper triangular
theorem UTMR, 1592
matrix representations
converting with change-of-basis
example MRCM, 1593
example OLTTR, 1594
matrix scalar multiplication
example MSM, 1595
matrix vector space
dimension
theorem DM, 1596
matrix-adjoint product
eigenvalues, eigenvectors
theorem EEMAP, 1597
matrix-vector product
example MTV, 1598
notation, 1599
MBC (example), 1600
MBLT (theorem), 1601
MC (notation), 1602
MCC (subsection, section MO), 1603
MCCN (Property), 1604
MCF (Property), 1605
MCN (definition), 1606
MCN (subsection, section CNO), 1607
MCSM (example), 1608
MCT (theorem), 1609
MD (chapter), 1610
ME (definition), 1611
ME (notation), 1612
ME (subsection, section PEE), 1613
ME (technique, section PT), 1614
ME (theorem), 1615
ME.MMA (computation, section MMA), 1616
ME.SAGE (computation, section SAGE), 1617
ME.TI83 (computation, section TI83), 1618
ME.TI86 (computation, section TI86), 1619
MEASM (subsection, section MO), 1620
MFLT (example), 1621
MI (definition), 1622
MI (example), 1623
MI (notation), 1624
MI.MMA (computation, section MMA), 1625
MI.SAGE (computation, section SAGE), 1626
MICN (Property), 1627
MIF (Property), 1628
MIMI (theorem), 1629
MINM (section), 1630
MISLE (section), 1631
MISM (theorem), 1632
MIT (theorem), 1633
MIU (theorem), 1634
MIVS (example), 1635
MLT (subsection, section LT), 1636
MLTCV (theorem), 1637
MLTLT (theorem), 1638
MM (definition), 1639
MM (section), 1640
MM (subsection, section MM), 1641
MM.MMA (computation, section MMA), 1642
MMA (section), 1643
MMA (theorem), 1644
MMAD (theorem), 1645
MMCC (theorem), 1646
MMDAA (theorem), 1647
MMEE (subsection, section MM), 1648
MMIM (theorem), 1649
MMIP (theorem), 1650
MMNC (example), 1651
MMSMM (theorem), 1652
MMT (theorem), 1653
MMZM (theorem), 1654
MNEM (theorem), 1655
MNSLE (example), 1656
MO (section), 1657
MOLT (example), 1658
more variables than equations
example OSGMD, 1659
theorem CMVEI, 1660
MPMR (example), 1661
MR (definition), 1662
MR (notation), 1663
MR (section), 1664
MRBE (example), 1665
MRCB (theorem), 1666
MRCLT (diagram), 1667
MRCLT (theorem), 1668
MRCM (example), 1669
MRLS (definition), 1670
MRLS (notation), 1671
MRMLT (theorem), 1672
MRRGE (theorem), 1673
MRS (subsection, section CB), 1674
MRSLT (theorem), 1675
MSCN (example), 1676
MSM (definition), 1677
MSM (example), 1678
MSM (notation), 1679
MTV (example), 1680
multiplicative associativity
complex numbers
Property MACN, 1681
multiplicative closure
complex numbers
Property MCCN, 1682
field
Property MCF, 1683
multiplicative commuativity
complex numbers
Property CMCN, 1684
multiplicative inverse
complex numbers
Property MICN, 1685
MVNSE (subsection, section RREF), 1686
MVP (definition), 1687
MVP (notation), 1688
MVP (subsection, section MM), 1689
MVSLD (theorem), 1690
MWIAA (example), 1691
N (archetype), 1692
N (subsection, section O), 1693
N (technique, section PT), 1694
NDMS4 (example), 1695
negation of statements
technique N, 1696
NEM (theorem), 1697
NI (theorem), 1698
NIAO (example), 1699
NIAQ (example), 1700
NIAQR (example), 1701
NIDAU (example), 1702
nilpotent
linear transformation
definition NLT, 1703
NILT (diagram), 1704
NJB (theorem), 1705
NJB5 (example), 1706
NKAO (example), 1707
NLT (definition), 1708
NLT (example), 1709
NLT (section), 1710
NLT (subsection, section NLT), 1711
NLTFO (subsection, section LT), 1712
NM (definition), 1713
NM (example), 1714
NM (section), 1715
NM (subsection, section NM), 1716
NM (subsection, section OD), 1717
NM62 (example), 1718
NM64 (example), 1719
NM83 (example), 1720
NME1 (theorem), 1721
NME2 (theorem), 1722
NME3 (theorem), 1723
NME4 (theorem), 1724
NME5 (theorem), 1725
NME6 (theorem), 1726
NME7 (theorem), 1727
NME8 (theorem), 1728
NME9 (theorem), 1729
NMI (subsection, section MINM), 1730
NMLIC (theorem), 1731
NMPEM (theorem), 1732
NMRRI (theorem), 1733
NMTNS (theorem), 1734
NMUS (theorem), 1735
NOILT (theorem), 1736
NOLT (definition), 1737
NOLT (notation), 1738
NOM (definition), 1739
NOM (notation), 1740
nonsingular
columns as basis
theorem CNMB, 1741
nonsingular matrices
linearly independent columns
theorem NMLIC, 1742
nonsingular matrix
Archetype B
example NM, 1743
column space, 1744
elemntary matrices
theorem NMPEM, 1745
equivalences
theorem NME1, 1746
theorem NME2, 1747
theorem NME3, 1748
theorem NME4, 1749
theorem NME5, 1750
theorem NME6, 1751
theorem NME7, 1752
theorem NME8, 1753
theorem NME9, 1754
matrix inverse, 1755
null space
example NSNM, 1756
nullity, 1757
product of nonsingular matrices
theorem NPNT, 1758
rank
theorem RNNM, 1759
row-reduced
theorem NMRRI, 1760
trivial null space
theorem NMTNS, 1761
unique solutions
theorem NMUS, 1762
nonsingular matrix, row-reduced
example NSR, 1763
norm
example CNSV, 1764
inner product, 1765
notation, 1766
normal matrix
definition NRML, 1767
example ANM, 1768
orthonormal basis, 1769
notation
A, 1770
AM, 1771
AME, 1772
C, 1773
CCCV, 1774
CCM, 1775
CCN, 1776
CNA, 1777
CNE, 1778
CNM, 1779
CSM, 1780
CV, 1781
CVA, 1782
CVC, 1783
CVE, 1784
CVSM, 1785
D, 1786
DM, 1787
DS, 1788
ELEM, 1789
ES, 1790
GES, 1791
GME, 1792
HI, 1793
HID, 1794
HP, 1795
IE, 1796
IM, 1797
IP, 1798
JB, 1799
KLT, 1800
LNS, 1801
LT, 1802
LTR, 1803
M, 1804
MA, 1805
MC, 1806
ME, 1807
MI, 1808
MR, 1809
MRLS, 1810
MSM, 1811
MVP, 1812
NOLT, 1813
NOM, 1814
NSM, 1815
NV, 1816
RLT, 1817
RO, 1818
ROLT, 1819
ROM, 1820
RREFA, 1821
RSM, 1822
SC, 1823
SE, 1824
SETM, 1825
SI, 1826
SM, 1827
SRM, 1828
SSET, 1829
SSV, 1830
SU, 1831
SUV, 1832
T, 1833
TM, 1834
VR, 1835
VSCV, 1836
VSM, 1837
ZCV, 1838
ZM, 1839
notation for a linear system
example NSE, 1840
NPNT (theorem), 1841
NRFO (subsection, section MR), 1842
NRML (definition), 1843
NRREF (example), 1844
NS.MMA (computation, section MMA), 1845
NSAO (example), 1846
NSAQ (example), 1847
NSAQR (example), 1848
NSC2A (example), 1849
NSC2S (example), 1850
NSC2Z (example), 1851
NSDAT (example), 1852
NSDS (example), 1853
NSE (example), 1854
NSEAI (example), 1855
NSLE (example), 1856
NSLIL (example), 1857
NSM (definition), 1858
NSM (notation), 1859
NSM (subsection, section HSE), 1860
NSMS (theorem), 1861
NSNM (example), 1862
NSNM (subsection, section NM), 1863
NSR (example), 1864
NSS (example), 1865
NSSLI (subsection, section LI), 1866
Null space
as a span
example NSDS, 1867
null space
Archetype I
example NSEAI, 1868
basis
theorem BNS, 1869
computation
example CNS1, 1870
example CNS2, 1871
isomorphic to kernel, 1872
linearly independent basis
example LINSB, 1873
mathematica, 1874
matrix
definition NSM, 1875
nonsingular matrix, 1876
notation, 1877
singular matrix, 1878
spanning set
example SSNS, 1879
theorem SSNS, 1880
subspace
theorem NSMS, 1881
null space span, linearly independent
Archetype L
example NSLIL, 1882
nullity
computing, 1883
injective linear transformation
theorem NOILT, 1884
linear transformation
definition NOLT, 1885
matrix, 1886
definition NOM, 1887
notation, 1888, 1889
square matrix, 1890
NV (definition), 1891
NV (notation), 1892
NVM (theorem), 1893
O (archetype), 1894
O (Property), 1895
O (section), 1896
OBC (subsection, section B), 1897
OBNM (theorem), 1898
OBUTR (theorem), 1899
OC (Property), 1900
OCN (Property), 1901
OD (section), 1902
OD (subsection, section OD), 1903
OD (theorem), 1904
OF (Property), 1905
OLTTR (example), 1906
OM (Property), 1907
one
column vectors
Property OC, 1908
complex numbers
Property OCN, 1909
field
Property OF, 1910
matrices
Property OM, 1911
vectors
Property O, 1912
ONFV (example), 1913
ONS (definition), 1914
ONTV (example), 1915
orthogonal
linear independence
theorem OSLI, 1916
set
example AOS, 1917
set of vectors
definition OSV, 1918
vector pairs
definition OV, 1919
orthogonal vectors
example TOV, 1920
orthonormal
definition ONS, 1921
matrix columns
example OSMC, 1922
orthonormal basis
normal matrix
theorem OBNM, 1923
orthonormal diagonalization
theorem OD, 1924
orthonormal set
four vectors
example ONFV, 1925
three vectors
example ONTV, 1926
OSGMD (example), 1927
OSIS (theorem), 1928
OSLI (theorem), 1929
OSMC (example), 1930
OSV (definition), 1931
OV (definition), 1932
OV (subsection, section O), 1933
P (appendix), 1934
P (archetype), 1935
P (technique, section PT), 1936
particular solutions
example PSHS, 1937
PCNA (theorem), 1938
PCVS (example), 1939
PD (section), 1940
PDM (section), 1941
PDM (theorem), 1942
PEE (section), 1943
PEEF (theorem), 1944
PI (definition), 1945
PI (subsection, section LT), 1946
PI (technique, section PT), 1947
PIP (theorem), 1948
PM (example), 1949
PM (subsection, section EE), 1950
PMI (subsection, section MISLE), 1951
PMM (subsection, section MM), 1952
PMR (subsection, section MR), 1953
PNLT (subsection, section NLT), 1954
POD (section), 1955
polar decomposition
theorem PDM, 1956
polynomial
of a matrix
example PM, 1957
polynomial vector space
dimension
theorem DP, 1958
positive semi-definite
creating
theorem CPSM, 1959
positive semi-definite matrix
definition PSM, 1960
eigenvalues
theorem EPSM, 1961
practice
technique P, 1962
pre-image
definition PI, 1963
kernel
theorem KPI, 1964
pre-images
example SPIAS, 1965
principal axis theorem, 1966
product of triangular matrices
theorem PTMT, 1967
Property
AA, 1968
AAC, 1969
AACN, 1970
AAF, 1971
AAM, 1972
AC, 1973
ACC, 1974
ACCN, 1975
ACF, 1976
ACM, 1977
AI, 1978
AIC, 1979
AICN, 1980
AIF, 1981
AIM, 1982
C, 1983
CACN, 1984
CAF, 1985
CC, 1986
CM, 1987
CMCN, 1988
CMF, 1989
DCN, 1990
DF, 1991
DMAM, 1992
DSA, 1993
DSAC, 1994
DSAM, 1995
DVA, 1996
DVAC, 1997
MACN, 1998
MAF, 1999
MCCN, 2000
MCF, 2001
MICN, 2002
MIF, 2003
O, 2004
OC, 2005
OCN, 2006
OF, 2007
OM, 2008
SC, 2009
SCC, 2010
SCM, 2011
SMA, 2012
SMAC, 2013
SMAM, 2014
Z, 2015
ZC, 2016
ZCN, 2017
ZF, 2018
ZM, 2019
PSHS (example), 2020
PSHS (subsection, section LC), 2021
PSM (definition), 2022
PSM (section), 2023
PSM (subsection, section PSM), 2024
PSM (subsection, section SD), 2025
PSMSR (theorem), 2026
PSPHS (theorem), 2027
PSS (subsection, section SSLE), 2028
PSSD (theorem), 2029
PSSLS (theorem), 2030
PT (section), 2031
PTFP (example), 2032
PTM (example), 2033
PTMEE (example), 2034
PTMT (theorem), 2035
Q (archetype), 2036
R (acronyms, section JCF), 2037
R (archetype), 2038
R (chapter), 2039
R.SAGE (computation, section SAGE), 2040
range
full
example FRAN, 2041
isomorphic to column space
theorem RCSI, 2042
linear transformation
example RAO, 2043
notation, 2044
of a linear transformation
definition RLT, 2045
pre-image
theorem RPI, 2046
subspace
theorem RLTS, 2047
surjective linear transformation
theorem RSLT, 2048
via matrix representation
example RVMR, 2049
rank
computing
theorem CRN, 2050
linear transformation
definition ROLT, 2051
matrix
definition ROM, 2052
example RNM, 2053
notation, 2054, 2055
of transpose
example RRTI, 2056
square matrix
example RNSM, 2057
surjective linear transformation
theorem ROSLT, 2058
transpose
theorem RMRT, 2059
rank one decomposition
size 2
example ROD2, 2060
size 4
example ROD4, 2061
theorem ROD, 2062
rank+nullity
theorem RPNC, 2063
RAO (example), 2064
RCLS (theorem), 2065
RCSI (theorem), 2066
RD (subsection, section VS), 2067
RDS (theorem), 2068
READ (subsection, section B), 2069
READ (subsection, section CB), 2070
READ (subsection, section CRS), 2071
READ (subsection, section D), 2072
READ (subsection, section DM), 2073
READ (subsection, section EE), 2074
READ (subsection, section FS), 2075
READ (subsection, section HSE), 2076
READ (subsection, section ILT), 2077
READ (subsection, section IVLT), 2078
READ (subsection, section LC), 2079
READ (subsection, section LDS), 2080
READ (subsection, section LI), 2081
READ (subsection, section LISS), 2082
READ (subsection, section LT), 2083
READ (subsection, section MINM), 2084
READ (subsection, section MISLE), 2085
READ (subsection, section MM), 2086
READ (subsection, section MO), 2087
READ (subsection, section MR), 2088
READ (subsection, section NM), 2089
READ (subsection, section O), 2090
READ (subsection, section PD), 2091
READ (subsection, section PDM), 2092
READ (subsection, section PEE), 2093
READ (subsection, section RREF), 2094
READ (subsection, section S), 2095
READ (subsection, section SD), 2096
READ (subsection, section SLT), 2097
READ (subsection, section SS), 2098
READ (subsection, section SSLE), 2099
READ (subsection, section TSS), 2100
READ (subsection, section VO), 2101
READ (subsection, section VR), 2102
READ (subsection, section VS), 2103
READ (subsection, section WILA), 2104
reduced row-echelon form
analysis
notation, 2105
definition RREF, 2106
example NRREF, 2107
example RREF, 2108
extended
definition EEF, 2109
notation
example RREFN, 2110
unique
theorem RREFU, 2111
reducing a span
example RSC5, 2112
relation of linear dependence
definition RLD, 2113
definition RLDCV, 2114
REM (definition), 2115
REMEF (theorem), 2116
REMES (theorem), 2117
REMRS (theorem), 2118
RES (example), 2119
RGEN (theorem), 2120
rings
sage, 2121
RLD (definition), 2122
RLDCV (definition), 2123
RLT (definition), 2124
RLT (notation), 2125
RLT (subsection, section IS), 2126
RLT (subsection, section SLT), 2127
RLTS (theorem), 2128
RMRT (theorem), 2129
RNLT (subsection, section IVLT), 2130
RNM (example), 2131
RNM (subsection, section D), 2132
RNNM (subsection, section D), 2133
RNNM (theorem), 2134
RNSM (example), 2135
RO (definition), 2136
RO (notation), 2137
RO (subsection, section RREF), 2138
ROD (section), 2139
ROD (theorem), 2140
ROD2 (example), 2141
ROD4 (example), 2142
ROLT (definition), 2143
ROLT (notation), 2144
ROM (definition), 2145
ROM (notation), 2146
ROSLT (theorem), 2147
row operations
definition RO, 2148
elementary matrices, 2149, 2150
notation, 2151
row reduce
mathematica, 2152
ti83, 2153
ti86, 2154
row space
Archetype I
example RSAI, 2155
as column space, 2156
basis
example RSB, 2157
theorem BRS, 2158
matrix, 2159
notation, 2160
row-equivalent matrices
theorem REMRS, 2161
subspace
theorem RSMS, 2162
row-equivalent matrices
definition REM, 2163
example TREM, 2164
row space, 2165
row spaces
example RSREM, 2166
theorem REMES, 2167
row-reduce
the verb
definition RR, 2168
row-reduced matrices
theorem REMEF, 2169
RPI (theorem), 2170
RPNC (theorem), 2171
RPNDD (theorem), 2172
RR (definition), 2173
RR.MMA (computation, section MMA), 2174
RR.TI83 (computation, section TI83), 2175
RR.TI86 (computation, section TI86), 2176
RREF (definition), 2177
RREF (example), 2178
RREF (section), 2179
RREF (subsection, section RREF), 2180
RREFA (notation), 2181
RREFN (example), 2182
RREFU (theorem), 2183
RRTI (example), 2184
RS (example), 2185
RSAI (example), 2186
RSB (example), 2187
RSC5 (example), 2188
RSLT (theorem), 2189
RSM (definition), 2190
RSM (notation), 2191
RSM (subsection, section CRS), 2192
RSMS (theorem), 2193
RSNS (example), 2194
RSREM (example), 2195
RSSC4 (example), 2196
RT (subsection, section PD), 2197
RVMR (example), 2198
S (archetype), 2199
S (definition), 2200
S (example), 2201
S (section), 2202
SAA (example), 2203
SAB (example), 2204
SABMI (example), 2205
SAE (example), 2206
sage
eigenspaces (computation), 2207
matrix entry (computation), 2208
matrix inverse (computation), 2209
rings (computation), 2210
transpose of a matrix (computation), 2211
SAGE (section), 2212
SAN (example), 2213
SAR (example), 2214
SAS (section), 2215
SAV (example), 2216
SC (definition), 2217
SC (example), 2218
SC (notation), 2219
SC (Property), 2220
SC (subsection, section S), 2221
SC (subsection, section SET), 2222
SC3 (example), 2223
SCAA (example), 2224
SCAB (example), 2225
SCAD (example), 2226
scalar closure
column vectors
Property SCC, 2227
matrices
Property SCM, 2228
vectors
Property SC, 2229
scalar multiple
matrix inverse, 2230
scalar multiplication
zero scalar
theorem ZSSM, 2231
zero vector
theorem ZVSM, 2232
zero vector result
theorem SMEZV, 2233
scalar multiplication associativity
column vectors
Property SMAC, 2234
matrices
Property SMAM, 2235
vectors
Property SMA, 2236
SCB (theorem), 2237
SCC (Property), 2238
SCM (Property), 2239
SD (section), 2240
SDS (example), 2241
SE (definition), 2242
SE (notation), 2243
secret sharing
6 ways
example SS6W, 2244
SEE (example), 2245
SEEF (example), 2246
SER (theorem), 2247
set
cardinality
definition C, 2248
example CS, 2249
notation, 2250
complement
definition SC, 2251
example SC, 2252
notation, 2253
definition SET, 2254
empty
definition ES, 2255
equality
definition SE, 2256
notation, 2257
intersection
definition SI, 2258
example SI, 2259
notation, 2260
membership
example SETM, 2261
notation, 2262
size, 2263
subset, 2264
union
definition SU, 2265
example SU, 2266
notation, 2267
SET (definition), 2268
SET (section), 2269
SETM (example), 2270
SETM (notation), 2271
shoes, 2272
SHS (subsection, section HSE), 2273
SI (definition), 2274
SI (example), 2275
SI (notation), 2276
SI (subsection, section IVLT), 2277
SIM (definition), 2278
similar matrices
equal eigenvalues
example EENS, 2279
eual eigenvalues
theorem SMEE, 2280
example SMS3, 2281
example SMS5, 2282
similarity
definition SIM, 2283
equivalence relation
theorem SER, 2284
singular matrix
Archetype A
example S, 2285
null space
example NSS, 2286
singular matrix, row-reduced
example SRR, 2287
singular value decomposition
theorem SVD, 2288
singular values
definition SV, 2289
SLE (acronyms, section NM), 2290
SLE (chapter), 2291
SLE (definition), 2292
SLE (subsection, section SSLE), 2293
SLELT (subsection, section IVLT), 2294
SLEMM (theorem), 2295
SLSLC (theorem), 2296
SLT (definition), 2297
SLT (section), 2298
SLTB (theorem), 2299
SLTD (subsection, section SLT), 2300
SLTD (theorem), 2301
SLTLT (theorem), 2302
SM (definition), 2303
SM (notation), 2304
SM (subsection, section SD), 2305
SM2Z7 (example), 2306
SM32 (example), 2307
SMA (Property), 2308
SMAC (Property), 2309
SMAM (Property), 2310
SMEE (theorem), 2311
SMEZV (theorem), 2312
SMLT (example), 2313
SMS (theorem), 2314
SMS3 (example), 2315
SMS5 (example), 2316
SMZD (theorem), 2317
SMZE (theorem), 2318
SNCM (theorem), 2319
SO (subsection, section SET), 2320
socks, 2321
SOL (subsection, section B), 2322
SOL (subsection, section CB), 2323
SOL (subsection, section CRS), 2324
SOL (subsection, section D), 2325
SOL (subsection, section DM), 2326
SOL (subsection, section EE), 2327
SOL (subsection, section F), 2328
SOL (subsection, section FS), 2329
SOL (subsection, section HSE), 2330
SOL (subsection, section ILT), 2331
SOL (subsection, section IVLT), 2332
SOL (subsection, section LC), 2333
SOL (subsection, section LDS), 2334
SOL (subsection, section LI), 2335
SOL (subsection, section LISS), 2336
SOL (subsection, section LT), 2337
SOL (subsection, section MINM), 2338
SOL (subsection, section MISLE), 2339
SOL (subsection, section MM), 2340
SOL (subsection, section MO), 2341
SOL (subsection, section MR), 2342
SOL (subsection, section NM), 2343
SOL (subsection, section O), 2344
SOL (subsection, section PD), 2345
SOL (subsection, section PDM), 2346
SOL (subsection, section PEE), 2347
SOL (subsection, section RREF), 2348
SOL (subsection, section S), 2349
SOL (subsection, section SD), 2350
SOL (subsection, section SLT), 2351
SOL (subsection, section SS), 2352
SOL (subsection, section SSLE), 2353
SOL (subsection, section T), 2354
SOL (subsection, section TSS), 2355
SOL (subsection, section VO), 2356
SOL (subsection, section VR), 2357
SOL (subsection, section VS), 2358
SOL (subsection, section WILA), 2359
solution set
Archetype A
example SAA, 2360
archetype E
example SAE, 2361
theorem PSPHS, 2362
solution sets
possibilities
theorem PSSLS, 2363
solution vector
definition SOLV, 2364
SOLV (definition), 2365
solving homogeneous system
Archetype A
example HISAA, 2366
Archetype B
example HUSAB, 2367
Archetype D
example HISAD, 2368
solving nonlinear equations
example STNE, 2369
SP4 (example), 2370
span
basic
example ABS, 2371
basis
theorem BS, 2372
definition SS, 2373
definition SSCV, 2374
improved
example IAS, 2375
notation, 2376
reducing
example RSSC4, 2377
reduction
example RS, 2378
removing vectors
example COV, 2379
reworking elements
example RES, 2380
set of polynomials
example SSP, 2381
subspace
theorem SSS, 2382
span of columns
Archetype A
example SCAA, 2383
Archetype B
example SCAB, 2384
Archetype D
example SCAD, 2385
spanning set
crazy vector space
example SSC, 2386
definition TSVS, 2387
matrices
example SSM22, 2388
more vectors
theorem SSLD, 2389
polynomials
example SSP4, 2390
SPIAS (example), 2391
SQM (definition), 2392
square root
eigenvalues, eigenspaces
theorem EESR, 2393
matrix
definition SRM, 2394
notation, 2395
positive semi-definite matrix
theorem PSMSR, 2396
unique
theorem USR, 2397
SR (section), 2398
SRM (definition), 2399
SRM (notation), 2400
SRM (subsection, section SR), 2401
SRR (example), 2402
SS (definition), 2403
SS (example), 2404
SS (section), 2405
SS (subsection, section LISS), 2406
SS (theorem), 2407
SS6W (example), 2408
SSC (example), 2409
SSCV (definition), 2410
SSET (definition), 2411
SSET (example), 2412
SSET (notation), 2413
SSLD (theorem), 2414
SSLE (section), 2415
SSM22 (example), 2416
SSNS (example), 2417
SSNS (subsection, section SS), 2418
SSNS (theorem), 2419
SSP (example), 2420
SSP4 (example), 2421
SSRLT (theorem), 2422
SSS (theorem), 2423
SSSLT (subsection, section SLT), 2424
SSV (notation), 2425
SSV (subsection, section SS), 2426
standard unit vector
notation, 2427
starting proofs
technique GS, 2428
STLT (example), 2429
STNE (example), 2430
SU (definition), 2431
SU (example), 2432
SU (notation), 2433
submatrix
notation, 2434
subset
definition SSET, 2435
notation, 2436
subspace
as null space
example RSNS, 2437
characterized
example ASC, 2438
definition S, 2439
in {P}_{4}
example SP4, 2440
not, additive closure
example NSC2A, 2441
not, scalar closure
example NSC2S, 2442
not, zero vector
example NSC2Z, 2443
testing
theorem TSS, 2444
trivial
definition TS, 2445
verification
example SC3, 2446
example SM32, 2447
subspaces
equal dimension
theorem EDYES, 2448
surjective
Archetype N
example SAN, 2449
example SAR, 2450
not
example NSAQ, 2451
example NSAQR, 2452
not, Archetype O
example NSAO, 2453
not, by dimension
example NSDAT, 2454
polynomials to matrices
example SAV, 2455
surjective linear transformation
bases
theorem SLTB, 2456
surjective linear transformations
dimension
theorem SLTD, 2457
SUV (definition), 2458
SUV (notation), 2459
SUVB (theorem), 2460
SUVOS (example), 2461
SV (definition), 2462
SVD (section), 2463
SVD (subsection, section SVD), 2464
SVD (theorem), 2465
SVP4 (example), 2466
SYM (definition), 2467
SYM (example), 2468
symmetric matrices
theorem SMS, 2469
symmetric matrix
example SYM, 2470
system of equations
vector equality
example VESE, 2471
system of linear equations
definition SLE, 2472
T (archetype), 2473
T (definition), 2474
T (notation), 2475
T (part), 2476
T (section), 2477
T (technique, section PT), 2478
TCSD (example), 2479
TD (section), 2480
TD (subsection, section TD), 2481
TD (theorem), 2482
TD4 (example), 2483
TDEE (theorem), 2484
TDEE6 (example), 2485
TDSSE (example), 2486
TDSSE (subsection, section TD), 2487
technique
C, 2488
CD, 2489
CP, 2490
CV, 2491
D, 2492
DC, 2493
E, 2494
GS, 2495
I, 2496
L, 2497
LC, 2498
ME, 2499
N, 2500
P, 2501
PI, 2502
T, 2503
U, 2504
theorem
AA, 2505
AIP, 2506
AISM, 2507
AIU, 2508
AMA, 2509
AMSM, 2510
BCS, 2511
BIS, 2512
BNS, 2513
BRS, 2514
BS, 2515
CB, 2516
CCM, 2517
CCRA, 2518
CCRM, 2519
CCT, 2520
CFDVS, 2521
CFNLT, 2522
CHT, 2523
CILTI, 2524
CINM, 2525
CIVLT, 2526
CLI, 2527
CLTLT, 2528
CMVEI, 2529
CNMB, 2530
COB, 2531
CPSM, 2532
CRMA, 2533
CRMSM, 2534
CRN, 2535
CRSM, 2536
CRVA, 2537
CSCS, 2538
CSLTS, 2539
CSMS, 2540
CSNM, 2541
CSRN, 2542
CSRST, 2543
CSS, 2544
CUMOS, 2545
DC, 2546
DCM, 2547
DCP, 2548
DEC, 2549
DED, 2550
DEM, 2551
DEMMM, 2552
DER, 2553
DERC, 2554
DFS, 2555
DGES, 2556
DIM, 2557
DLDS, 2558
DM, 2559
DMFE, 2560
DMHP, 2561
DMMP, 2562
DMST, 2563
DNLT, 2564
DP, 2565
DRCM, 2566
DRCMA, 2567
DRCS, 2568
DRMM, 2569
DSD, 2570
DSFB, 2571
DSFOS, 2572
DSLI, 2573
DSZI, 2574
DSZV, 2575
DT, 2576
DVM, 2577
DZRC, 2578
EDELI, 2579
EDYES, 2580
EEMAP, 2581
EER, 2582
EESR, 2583
EIM, 2584
EIS, 2585
ELIS, 2586
EMDRO, 2587
EMHE, 2588
EMMVP, 2589
EMN, 2590
EMNS, 2591
EMP, 2592
EMRCP, 2593
EMS, 2594
ENLT, 2595
EOMP, 2596
EOPSS, 2597
EPM, 2598
EPSM, 2599
ERMCP, 2600
ESMM, 2601
ETM, 2602
FIMP, 2603
FS, 2604
FTMR, 2605
FVCS, 2606
G, 2607
GEK, 2608
GESD, 2609
GESIS, 2610
GSP, 2611
HMIP, 2612
HMOE, 2613
HMRE, 2614
HMVEI, 2615
HPC, 2616
HPDAA, 2617
HPHI, 2618
HPHID, 2619
HPSMM, 2620
HSC, 2621
ICBM, 2622
ICLT, 2623
IFDVS, 2624
IILT, 2625
ILTB, 2626
ILTD, 2627
ILTIS, 2628
ILTLI, 2629
ILTLT, 2630
IMILT, 2631
IMR, 2632
IP, 2633
IPAC, 2634
IPN, 2635
IPSM, 2636
IPVA, 2637
ISRN, 2638
ITMT, 2639
IVSED, 2640
JCFLT, 2641
KILT, 2642
KLTS, 2643
KNSI, 2644
KPI, 2645
KPIS, 2646
KPLT, 2647
KPNLT, 2648
LIVHS, 2649
LIVRN, 2650
LNSMS, 2651
LSMR, 2652
LTDB, 2653
LTLC, 2654
LTTZZ, 2655
MBLT, 2656
MCT, 2657
ME, 2658
MIMI, 2659
MISM, 2660
MIT, 2661
MIU, 2662
MLTCV, 2663
MLTLT, 2664
MMA, 2665
MMAD, 2666
MMCC, 2667
MMDAA, 2668
MMIM, 2669
MMIP, 2670
MMSMM, 2671
MMT, 2672
MMZM, 2673
MNEM, 2674
MRCB, 2675
MRCLT, 2676
MRMLT, 2677
MRRGE, 2678
MRSLT, 2679
MVSLD, 2680
NEM, 2681
NI, 2682
NJB, 2683
NME1, 2684
NME2, 2685
NME3, 2686
NME4, 2687
NME5, 2688
NME6, 2689
NME7, 2690
NME8, 2691
NME9, 2692
NMLIC, 2693
NMPEM, 2694
NMRRI, 2695
NMTNS, 2696
NMUS, 2697
NOILT, 2698
NPNT, 2699
NSMS, 2700
NVM, 2701
OBNM, 2702
OBUTR, 2703
OD, 2704
OSIS, 2705
OSLI, 2706
PCNA, 2707
PDM, 2708
PEEF, 2709
PIP, 2710
PSMSR, 2711
PSPHS, 2712
PSSD, 2713
PSSLS, 2714
PTMT, 2715
RCLS, 2716
RCSI, 2717
RDS, 2718
REMEF, 2719
REMES, 2720
REMRS, 2721
RGEN, 2722
RLTS, 2723
RMRT, 2724
RNNM, 2725
ROD, 2726
ROSLT, 2727
RPI, 2728
RPNC, 2729
RPNDD, 2730
RREFU, 2731
RSLT, 2732
RSMS, 2733
SCB, 2734
SER, 2735
SLEMM, 2736
SLSLC, 2737
SLTB, 2738
SLTD, 2739
SLTLT, 2740
SMEE, 2741
SMEZV, 2742
SMS, 2743
SMZD, 2744
SMZE, 2745
SNCM, 2746
SS, 2747
SSLD, 2748
SSNS, 2749
SSRLT, 2750
SSS, 2751
SUVB, 2752
SVD, 2753
TD, 2754
TDEE, 2755
technique T, 2756
TIST, 2757
TL, 2758
TMA, 2759
TMSM, 2760
TSE, 2761
TSRM, 2762
TSS, 2763
TT, 2764
TTMI, 2765
UMCOB, 2766
UMI, 2767
UMPIP, 2768
USR, 2769
UTMR, 2770
VFSLS, 2771
VRI, 2772
VRILT, 2773
VRLT, 2774
VRRB, 2775
VRS, 2776
VSLT, 2777
VSPCV, 2778
VSPM, 2779
ZSSM, 2780
ZVSM, 2781
ZVU, 2782
ti83
matrix entry (computation), 2783
row reduce (computation), 2784
vector linear combinations (computation), 2785
TI83 (section), 2786
ti86
matrix entry (computation), 2787
row reduce (computation), 2788
transpose of a matrix (computation), 2789
vector linear combinations (computation), 2790
TI86 (section), 2791
TIS (example), 2792
TIST (theorem), 2793
TIVS (example), 2794
TKAP (example), 2795
TL (theorem), 2796
TLC (example), 2797
TM (definition), 2798
TM (example), 2799
TM (notation), 2800
TM (subsection, section OD), 2801
TM.MMA (computation, section MMA), 2802
TM.SAGE (computation, section SAGE), 2803
TM.TI86 (computation, section TI86), 2804
TMA (theorem), 2805
TMP (example), 2806
TMSM (theorem), 2807
TOV (example), 2808
trace
definition T, 2809
linearity
theorem TL, 2810
matrix multiplication
theorem TSRM, 2811
notation, 2812
similarity
theorem TIST, 2813
sum of eigenvalues
theorem TSE, 2814
trail mix
example TMP, 2815
transpose
matrix scalar multiplication
theorem TMSM, 2816
example TM, 2817
matrix addition
theorem TMA, 2818
matrix inverse, 2819, 2820
notation, 2821
scalar multiplication, 2822
transpose of a matrix
mathematica, 2823
sage, 2824
ti86, 2825
transpose of a transpose
theorem TT, 2826
TREM (example), 2827
triangular decomposition
entry by entry, size 6
example TDEE6, 2828
entry by entry
theorem TDEE, 2829
size 4
example TD4, 2830
solving systems of equations
example TDSSE, 2831
theorem TD, 2832
triangular matrix
inverse
theorem ITMT, 2833
trivial solution
system of equations
definition TSHSE, 2834
TS (definition), 2835
TS (subsection, section S), 2836
TSE (theorem), 2837
TSHSE (definition), 2838
TSM (subsection, section MO), 2839
TSRM (theorem), 2840
TSS (section), 2841
TSS (subsection, section S), 2842
TSS (theorem), 2843
TSVS (definition), 2844
TT (theorem), 2845
TTMI (theorem), 2846
TTS (example), 2847
typical systems, 2 × 2
example TTS, 2848
U (archetype), 2849
U (technique, section PT), 2850
UM (definition), 2851
UM (subsection, section MINM), 2852
UM3 (example), 2853
UMCOB (theorem), 2854
UMI (theorem), 2855
UMPIP (theorem), 2856
unique solution, 3 × 3
example US, 2857
example USR, 2858
uniqueness
technique U, 2859
unit vectors
basis
theorem SUVB, 2860
definition SUV, 2861
orthogonal
example SUVOS, 2862
unitary
permutation matrix
example UPM, 2863
size 3
example UM3, 2864
unitary matrices
columns
theorem CUMOS, 2865
unitary matrix
inner product
theorem UMPIP, 2866
UPM (example), 2867
upper triangular matrix
definition UTM, 2868
US (example), 2869
USR (example), 2870
USR (theorem), 2871
UTM (definition), 2872
UTMR (subsection, section OD), 2873
UTMR (theorem), 2874
V (acronyms, section O), 2875
V (archetype), 2876
V (chapter), 2877
VA (example), 2878
Vandermonde matrix
definition VM, 2879
vandermonde matrix
determinant
theorem DVM, 2880
nonsingular
theorem NVM, 2881
size 4
example VM4, 2882
VEASM (subsection, section VO), 2883
vector
addition
definition CVA, 2884
column
definition CV, 2885
equality
definition CVE, 2886
notation, 2887
inner product
definition IP, 2888
norm
definition NV, 2889
notation, 2890
of constants
definition VOC, 2891
product with matrix, 2892, 2893
scalar multiplication
definition CVSM, 2894
vector addition
example VA, 2895
vector component
notation, 2896
vector form of solutions
Archetype D
example VFSAD, 2897
Archetype I
example VFSAI, 2898
Archetype L
example VFSAL, 2899
example VFS, 2900
mathematica, 2901
theorem VFSLS, 2902
vector linear combinations
mathematica, 2903
ti83, 2904
ti86, 2905
vector representation
example AVR, 2906
example VRC4, 2907
injective
theorem VRI, 2908
invertible
theorem VRILT, 2909
linear transformation
definition VR, 2910
notation, 2911
theorem VRLT, 2912
surjective
theorem VRS, 2913
theorem VRRB, 2914
vector representations
polynomials
example VRP2, 2915
vector scalar multiplication
example CVSM, 2916
vector space
characterization
theorem CFDVS, 2917
column vectors
definition VSCV, 2918
definition VS, 2919
infinite dimension
example VSPUD, 2920
linear transformations
theorem VSLT, 2921
over integers mod 5
example VSIM5, 2922
vector space of column vectors
notation, 2923
vector space of functions
example VSF, 2924
vector space of infinite sequences
example VSIS, 2925
vector space of matrices
definition VSM, 2926
example VSM, 2927
notation, 2928
vector space of polynomials
example VSP, 2929
vector space properties
column vectors
theorem VSPCV, 2930
matrices
theorem VSPM, 2931
vector space, crazy
example CVS, 2932
vector space, singleton
example VSS, 2933
vector spaces
isomorphic
definition IVS, 2934
theorem IFDVS, 2935
VESE (example), 2936
VFS (example), 2937
VFSAD (example), 2938
VFSAI (example), 2939
VFSAL (example), 2940
VFSLS (theorem), 2941
VFSS (subsection, section LC), 2942
VFSS.MMA (computation, section MMA), 2943
VLC.MMA (computation, section MMA), 2944
VLC.TI83 (computation, section TI83), 2945
VLC.TI86 (computation, section TI86), 2946
VM (definition), 2947
VM (section), 2948
VM4 (example), 2949
VO (section), 2950
VOC (definition), 2951
VR (definition), 2952
VR (notation), 2953
VR (section), 2954
VR (subsection, section LISS), 2955
VRC4 (example), 2956
VRI (theorem), 2957
VRILT (theorem), 2958
VRLT (theorem), 2959
VRP2 (example), 2960
VRRB (theorem), 2961
VRS (theorem), 2962
VS (acronyms, section PD), 2963
VS (chapter), 2964
VS (definition), 2965
VS (section), 2966
VS (subsection, section VS), 2967
VSCV (definition), 2968
VSCV (example), 2969
VSCV (notation), 2970
VSF (example), 2971
VSIM5 (example), 2972
VSIS (example), 2973
VSLT (theorem), 2974
VSM (definition), 2975
VSM (example), 2976
VSM (notation), 2977
VSP (example), 2978
VSP (subsection, section MO), 2979
VSP (subsection, section VO), 2980
VSP (subsection, section VS), 2981
VSPCV (theorem), 2982
VSPM (theorem), 2983
VSPUD (example), 2984
VSS (example), 2985
W (archetype), 2986
WILA (section), 2987
X (archetype), 2988
Z (Property), 2989
ZC (Property), 2990
ZCN (Property), 2991
ZCV (definition), 2992
ZCV (notation), 2993
zero
complex numbers
Property ZCN, 2994
field
Property ZF, 2995
zero column vector
definition ZCV, 2996
notation, 2997
zero matrix
notation, 2998
zero vector
column vectors
Property ZC, 2999
matrices
Property ZM, 3000
unique
theorem ZVU, 3001
vectors
Property Z, 3002
ZF (Property), 3003
ZM (definition), 3004
ZM (notation), 3005
ZM (Property), 3006
ZNDAB (example), 3007
ZSSM (theorem), 3008
ZVSM (theorem), 3009
ZVU (theorem), 3010