B (archetype), 88
B (definition), 89
B (section), 90
B (subsection, section B), 91
basis
columns nonsingular matrix
example CABAK, 92
common size
theorem BIS, 93
crazy vector apace
example BC, 94
definition B, 95
matrices
example BM, 96
example BSM22, 97
polynomials
example BP, 98
example BPR, 99
example BSP4, 100
example SVP4, 101
subspace of matrices
example BDM22, 102
BC (example), 103
BCS (theorem), 104
BDE (example), 105
BDM22 (example), 106
best cities
money magazine
example MBC, 107
BIS (theorem), 108
BM (example), 109
BNM (subsection, section B), 110
BNS (theorem), 111
BP (example), 112
BPR (example), 113
BRLT (example), 114
BRS (theorem), 115
BS (theorem), 116
BSCV (subsection, section B), 117
BSM22 (example), 118
BSP4 (example), 119
C (archetype), 120
C (definition), 121
C (notation), 122
C (part), 123
C (Property), 124
C (technique, section PT), 125
CABAK (example), 126
CAEHW (example), 127
cancellation
vector addition
theorem VAC, 128
canonical form
nilpotent linear transformation
example CFNLT, 129
theorem CFNLT, 130
CAV (subsection, section O), 131
Cayley-Hamilton
theorem CHT, 132
CB (section), 133
CB (theorem), 134
CBCV (example), 135
CBM (definition), 136
CBM (subsection, section CB), 137
CBP (example), 138
CC (Property), 139
CCCV (definition), 140
CCCV (notation), 141
CCM (definition), 142
CCM (example), 143
CCM (notation), 144
CCN (definition), 145
CCN (notation), 146
CCN (subsection, section CNO), 147
CCRA (theorem), 148
CCRM (theorem), 149
CCT (theorem), 150
CD (subsection, section DM), 151
CD (technique, section PT), 152
CEE (subsection, section EE), 153
CELT (example), 154
CELT (subsection, section CB), 155
CEMS6 (example), 156
CFDVS (theorem), 157
CFNLT (example), 158
CFNLT (subsection, section NLT), 159
CFNLT (theorem), 160
CFV (example), 161
change of basis
between polynomials
example CBP, 162
change-of-basis
between column vectors
example CBCV, 163
matrix representation
theorem MRCB, 164
similarity
theorem SCB, 165
theorem CB, 166
change-of-basis matrix
definition CBM, 167
inverse
theorem ICBM, 168
characteristic polynomial
definition CP, 169
degree
theorem DCP, 170
size 3 matrix
example CPMS3, 171
CHT (subsection, section JCF), 172
CHT (theorem), 173
CILT (subsection, section ILT), 174
CILTI (theorem), 175
CIM (subsection, section MISLE), 176
CINM (theorem), 177
CIVLT (theorem), 178
CLI (theorem), 179
CLTLT (theorem), 180
CM (definition), 181
CM (Property), 182
CM32 (example), 183
CMI (example), 184
CMIAB (example), 185
CMVEI (theorem), 186
CN (appendix), 187
CNA (definition), 188
CNA (notation), 189
CNA (subsection, section CNO), 190
CNE (definition), 191
CNE (notation), 192
CNM (definition), 193
CNM (notation), 194
CNMB (theorem), 195
CNO (section), 196
CNS1 (example), 197
CNS2 (example), 198
CNSV (example), 199
COB (theorem), 200
coefficient matrix
definition CM, 201
nonsingular
theorem SNCM, 202
column space
as null space
theorem FS, 203
Archetype A
example CSAA, 204
Archetype B
example CSAB, 205
as null space
example CSANS, 206
as null space, Archetype G
example FSAG, 207
as row space
theorem CSRST, 208
basis
theorem BCS, 209
consistent system
theorem CSCS, 210
consistent systems
example CSMCS, 211
isomorphic to range, 212
matrix, 213
nonsingular matrix
theorem CSNM, 214
notation, 215
original columns, Archetype D
example CSOCD, 216
row operations, Archetype I
example CSROI, 217
subspace
theorem CSMS, 218
testing membership
example MCSM, 219
two computations
example CSTW, 220
column vector addition
notation, 221
column vector scalar multiplication
notation, 222
commutativity
column vectors
Property CC, 223
matrices
Property CM, 224
vectors
Property C, 225
complex -space
example VSCV, 226
complex arithmetic
example ACN, 227
complex number
conjugate
example CSCN, 228
modulus
example MSCN, 229
complex number
conjugate
definition CCN, 230
modulus
definition MCN, 231
complex numbers
addition
definition CNA, 232
notation, 233
arithmetic properties
theorem PCNA, 234
equality
definition CNE, 235
notation, 236
multiplication
definition CNM, 237
notation, 238
complex vector space
dimension
theorem DCM, 239
composition
injective linear transformations
theorem CILTI, 240
surjective linear transformations
theorem CSLTS, 241
conjugate
addition
theorem CCRA, 242
column vector
definition CCCV, 243
matrix
definition CCM, 244
notation, 245
multiplication
theorem CCRM, 246
notation, 247
scalar multiplication
theorem CRSM, 248
twice
theorem CCT, 249
vector addition
theorem CRVA, 250
conjugate of a vector
notation, 251
conjugation
matrix addition
theorem CRMA, 252
matrix scalar multiplication
theorem CRMSM, 253
matrix transpose
theorem MCT, 254
consistent linear system, 255
consistent linear systems
theorem CSRN, 256
consistent system
definition CS, 257
constructive proofs
technique C, 258
contradiction
technique CD, 259
contrapositive
technique CP, 260
converse
technique CV, 261
coordinates
orthonormal basis
theorem COB, 262
coordinatization
linear combination of matrices
example CM32, 263
linear independence
theorem CLI, 264
orthonormal basis
example CROB3, 265
example CROB4, 266
spanning sets
theorem CSS, 267
coordinatization principle, 268
coordinatizing
polynomials
example CP2, 269
COV (example), 270
COV (subsection, section LDS), 271
CP (definition), 272
CP (subsection, section VR), 273
CP (technique, section PT), 274
CP2 (example), 275
CPMS3 (example), 276
crazy vector space
example CVSR, 277
properties
example PCVS, 278
CRMA (theorem), 279
CRMSM (theorem), 280
CRN (theorem), 281
CROB3 (example), 282
CROB4 (example), 283
CRS (section), 284
CRS (subsection, section FS), 285
CRSM (theorem), 286
CRVA (theorem), 287
CS (definition), 288
CS (example), 289
CS (subsection, section TSS), 290
CSAA (example), 291
CSAB (example), 292
CSANS (example), 293
CSCN (example), 294
CSCS (theorem), 295
CSIP (example), 296
CSLT (subsection, section SLT), 297
CSLTS (theorem), 298
CSM (definition), 299
CSM (notation), 300
CSMCS (example), 301
CSMS (theorem), 302
CSNM (subsection, section CRS), 303
CSNM (theorem), 304
CSOCD (example), 305
CSRN (theorem), 306
CSROI (example), 307
CSRST (theorem), 308
CSS (theorem), 309
CSSE (subsection, section CRS), 310
CSSM (theorem), 311
CSSOC (subsection, section CRS), 312
CSTW (example), 313
CTD (subsection, section TD), 314
CTLT (example), 315
CUMOS (theorem), 316
CV (definition), 317
CV (notation), 318
CV (technique, section PT), 319
CVA (definition), 320
CVA (notation), 321
CVC (notation), 322
CVE (definition), 323
CVE (notation), 324
CVS (example), 325
CVS (subsection, section VR), 326
CVSM (definition), 327
CVSM (example), 328
CVSM (notation), 329
CVSM (theorem), 330
CVSR (example), 331
D (archetype), 332
D (chapter), 333
D (definition), 334
D (notation), 335
D (section), 336
D (subsection, section D), 337
D (subsection, section SD), 338
D (technique, section PT), 339
D33M (example), 340
DAB (example), 341
DC (example), 342
DC (technique, section PT), 343
DC (theorem), 344
DCM (theorem), 345
DCN (Property), 346
DCP (theorem), 347
DD (subsection, section DM), 348
DEC (theorem), 349
decomposition
technique DC, 350
DED (theorem), 351
definition
A, 352
AM, 353
AME, 354
B, 355
C, 356
CBM, 357
CCCV, 358
CCM, 359
CCN, 360
CM, 361
CNA, 362
CNE, 363
CNM, 364
CP, 365
CS, 366
CSM, 367
CV, 368
CVA, 369
CVE, 370
CVSM, 371
D, 372
DIM, 373
DM, 374
DS, 375
DZM, 376
EEF, 377
EELT, 378
EEM, 379
ELEM, 380
EM, 381
EO, 382
ES, 383
ESYS, 384
F, 385
GES, 386
GEV, 387
GME, 388
HM, 389
HS, 390
IDLT, 391
IDV, 392
IE, 393
ILT, 394
IM, 395
IMP, 396
IP, 397
IS, 398
IVLT, 399
IVS, 400
JB, 401
JCF, 402
KLT, 403
LC, 404
LCCV, 405
LI, 406
LICV, 407
LNS, 408
LSMR, 409
LT, 410
LTA, 411
LTC, 412
LTM, 413
LTR, 414
LTSM, 415
M, 416
MA, 417
MCN, 418
ME, 419
MI, 420
MM, 421
MR, 422
MSM, 423
MVP, 424
NLT, 425
NM, 426
NOLT, 427
NOM, 428
NRML, 429
NSM, 430
NV, 431
ONS, 432
OSV, 433
OV, 434
PI, 435
REM, 436
RLD, 437
RLDCV, 438
RLT, 439
RO, 440
ROLT, 441
ROM, 442
RR, 443
RREF, 444
RSM, 445
S, 446
SC, 447
SE, 448
SET, 449
SI, 450
SIM, 451
SLE, 452
SLT, 453
SM, 454
SQM, 455
SS, 456
SSCV, 457
SSET, 458
SU, 459
SUV, 460
SV, 461
SYM, 462
technique D, 463
TM, 464
TS, 465
TSHSE, 466
TSVS, 467
UM, 468
UTM, 469
VOC, 470
VR, 471
VS, 472
VSCV, 473
VSM, 474
ZCV, 475
ZM, 476
DEHD (example), 477
DEM (theorem), 478
DEMMM (theorem), 479
DEMS5 (example), 480
DER (theorem), 481
DERC (theorem), 482
determinant
computed two ways
example TCSD, 483
definition DM, 484
equal rows or columns
theorem DERC, 485
expansion, columns
theorem DEC, 486
expansion, rows
theorem DER, 487
identity matrix
theorem DIM, 488
matrix multiplication
theorem DRMM, 489
nonsingular matrix, 490
notation, 491
row or column multiple
theorem DRCM, 492
row or column swap
theorem DRCS, 493
size 2 matrix
theorem DMST, 494
size 3 matrix
example D33M, 495
transpose
theorem DT, 496
via row operations
example DRO, 497
zero
theorem SMZD, 498
zero row or column
theorem DZRC, 499
zero versus nonzero
example ZNDAB, 500
determinant, upper triangular matrix
example DUTM, 501
determinants
elementary matrices
theorem DEMMM, 502
DF (Property), 503
DFS (subsection, section PD), 504
DFS (theorem), 505
DGES (theorem), 506
diagonal matrix
definition DIM, 507
diagonalizable
definition DZM, 508
distinct eigenvalues
example DEHD, 509
theorem DED, 510
full eigenspaces
theorem DMFE, 511
not
example NDMS4, 512
diagonalizable matrix
high power
example HPDM, 513
diagonalization
Archetype B
example DAB, 514
criteria
theorem DC, 515
example DMS3, 516
DIM (definition), 517
DIM (theorem), 518
dimension
crazy vector space
example DC, 519
definition D, 520
notation, 521
polynomial subspace
example DSP4, 522
proper subspaces
theorem PSSD, 523
subspace
example DSM22, 524
direct sum
decomposing zero vector
theorem DSZV, 525
definition DS, 526
dimension
theorem DSD, 527
example SDS, 528
from a basis
theorem DSFB, 529
from one subspace
theorem DSFOS, 530
notation, 531
zero intersection
theorem DSZI, 532
direct sums
linear independence
theorem DSLI, 533
repeated
theorem RDS, 534
distributivity
complex numbers
Property DCN, 535
field
Property DF, 536
distributivity, matrix addition
matrices
Property DMAM, 537
distributivity, scalar addition
column vectors
Property DSAC, 538
matrices
Property DSAM, 539
vectors
Property DSA, 540
distributivity, vector addition
column vectors
Property DVAC, 541
vectors
Property DVA, 542
DLDS (theorem), 543
DM (definition), 544
DM (notation), 545
DM (section), 546
DM (theorem), 547
DMAM (Property), 548
DMFE (theorem), 549
DMS3 (example), 550
DMST (theorem), 551
DNLT (theorem), 552
DNMMM (subsection, section PDM), 553
DP (theorem), 554
DRCM (theorem), 555
DRCMA (theorem), 556
DRCS (theorem), 557
DRMM (theorem), 558
DRO (example), 559
DRO (subsection, section PDM), 560
DROEM (subsection, section PDM), 561
DS (definition), 562
DS (notation), 563
DS (subsection, section PD), 564
DSA (Property), 565
DSAC (Property), 566
DSAM (Property), 567
DSD (theorem), 568
DSFB (theorem), 569
DSFOS (theorem), 570
DSLI (theorem), 571
DSM22 (example), 572
DSP4 (example), 573
DSZI (theorem), 574
DSZV (theorem), 575
DT (theorem), 576
DUTM (example), 577
DVA (Property), 578
DVAC (Property), 579
DVS (subsection, section D), 580
DZM (definition), 581
DZRC (theorem), 582
E (archetype), 583
E (chapter), 584
E (technique, section PT), 585
ECEE (subsection, section EE), 586
EDELI (theorem), 587
EDYES (theorem), 588
EE (section), 589
EEE (subsection, section EE), 590
EEF (definition), 591
EEF (subsection, section FS), 592
EELT (definition), 593
EELT (subsection, section CB), 594
EEM (definition), 595
EEM (subsection, section EE), 596
EENS (example), 597
EER (theorem), 598
EHM (subsection, section PEE), 599
eigenspace
as null space
theorem EMNS, 600
definition EM, 601
invariant subspace
theorem EIS, 602
subspace
theorem EMS, 603
eigenvalue
algebraic multiplicity
definition AME, 604
complex
example CEMS6, 605
definition EEM, 606
existence
example CAEHW, 607
theorem EMHE, 608
geometric multiplicity
definition GME, 609
index, 610
linear transformation
definition EELT, 611
multiplicities
example EMMS4, 612
power
theorem EOMP, 613
root of characteristic polynomial
theorem EMRCP, 614
scalar multiple
theorem ESMM, 615
symmetric matrix
example ESMS4, 616
zero
theorem SMZE, 617
eigenvalues
building desired
example BDE, 618
complex, of a linear transformation
example CELT, 619
conjugate pairs
theorem ERMCP, 620
distinct
example DEMS5, 621
example SEE, 622
Hermitian matrices
theorem HMRE, 623
inverse
theorem EIM, 624
maximum number
theorem MNEM, 625
multiplicities
example HMEM5, 626
theorem ME, 627
number
theorem NEM, 628
of a polynomial
theorem EPM, 629
size 3 matrix
example EMS3, 630
example ESMS3, 631
transpose
theorem ETM, 632
eigenvalues, eigenvectors
vector, matrix representations
theorem EER, 633
eigenvector, 634
linear transformation, 635
eigenvectors, 636
conjugate pairs, 637
Hermitian matrices
theorem HMOE, 638
linear transformation
example ELTBM, 639
example ELTBP, 640
linearly independent
theorem EDELI, 641
of a linear transformation
example ELTT, 642
EILT (subsection, section ILT), 643
EIM (theorem), 644
EIS (example), 645
EIS (theorem), 646
ELEM (definition), 647
ELEM (notation), 648
elementary matrices
definition ELEM, 649
determinants
theorem DEM, 650
nonsingular
theorem EMN, 651
notation, 652
row operations
example EMRO, 653
theorem EMDRO, 654
ELIS (theorem), 655
ELTBM (example), 656
ELTBP (example), 657
ELTT (example), 658
EM (definition), 659
EM (subsection, section DM), 660
EMDRO (theorem), 661
EMHE (theorem), 662
EMMS4 (example), 663
EMMVP (theorem), 664
EMN (theorem), 665
EMNS (theorem), 666
EMP (theorem), 667
empty set, 668
notation, 669
EMRCP (theorem), 670
EMRO (example), 671
EMS (theorem), 672
EMS3 (example), 673
ENLT (theorem), 674
EO (definition), 675
EOMP (theorem), 676
EOPSS (theorem), 677
EPM (theorem), 678
equal matrices
via equal matrix-vector products
theorem EMMVP, 679
equation operations
definition EO, 680
theorem EOPSS, 681
equivalence statements
technique E, 682
equivalences
technique ME, 683
equivalent systems
definition ESYS, 684
ERMCP (theorem), 685
ES (definition), 686
ES (notation), 687
ESEO (subsection, section SSLE), 688
ESLT (subsection, section SLT), 689
ESMM (theorem), 690
ESMS3 (example), 691
ESMS4 (example), 692
ESYS (definition), 693
ETM (theorem), 694
EVS (subsection, section VS), 695
example
AALC, 696
ABLC, 697
ABS, 698
ACN, 699
AHSAC, 700
AIVLT, 701
ALT, 702
ALTMM, 703
AM, 704
AMAA, 705
ANILT, 706
ANM, 707
AOS, 708
ASC, 709
AVR, 710
BC, 711
BDE, 712
BDM22, 713
BM, 714
BP, 715
BPR, 716
BRLT, 717
BSM22, 718
BSP4, 719
CABAK, 720
CAEHW, 721
CBCV, 722
CBP, 723
CCM, 724
CELT, 725
CEMS6, 726
CFNLT, 727
CFV, 728
CM32, 729
CMI, 730
CMIAB, 731
CNS1, 732
CNS2, 733
CNSV, 734
COV, 735
CP2, 736
CPMS3, 737
CROB3, 738
CROB4, 739
CS, 740
CSAA, 741
CSAB, 742
CSANS, 743
CSCN, 744
CSIP, 745
CSMCS, 746
CSOCD, 747
CSROI, 748
CSTW, 749
CTLT, 750
CVS, 751
CVSM, 752
CVSR, 753
D33M, 754
DAB, 755
DC, 756
DEHD, 757
DEMS5, 758
DMS3, 759
DRO, 760
DSM22, 761
DSP4, 762
DUTM, 763
EENS, 764
EIS, 765
ELTBM, 766
ELTBP, 767
ELTT, 768
EMMS4, 769
EMRO, 770
EMS3, 771
ESMS3, 772
ESMS4, 773
FDV, 774
FF8, 775
FRAN, 776
FS1, 777
FS2, 778
FSAG, 779
GE4, 780
GE6, 781
GENR6, 782
GSTV, 783
HISAA, 784
HISAD, 785
HMEM5, 786
HPDM, 787
HUSAB, 788
IAP, 789
IAR, 790
IAS, 791
IAV, 792
ILTVR, 793
IM, 794
IM11, 795
IS, 796
ISJB, 797
ISMR4, 798
ISMR6, 799
ISSI, 800
IVSAV, 801
JB4, 802
JCF10, 803
KPNLT, 804
KVMR, 805
LCM, 806
LDCAA, 807
LDHS, 808
LDP4, 809
LDRN, 810
LDS, 811
LIC, 812
LICAB, 813
LIHS, 814
LIM32, 815
LINSB, 816
LIP4, 817
LIS, 818
LLDS, 819
LNS, 820
LTDB1, 821
LTDB2, 822
LTDB3, 823
LTM, 824
LTPM, 825
LTPP, 826
LTRGE, 827
MA, 828
MBC, 829
MCSM, 830
MFLT, 831
MI, 832
MIVS, 833
MMNC, 834
MNSLE, 835
MOLT, 836
MPMR, 837
MRBE, 838
MRCM, 839
MSCN, 840
MSM, 841
MTV, 842
MWIAA, 843
NDMS4, 844
NIAO, 845
NIAQ, 846
NIAQR, 847
NIDAU, 848
NJB5, 849
NKAO, 850
NLT, 851
NM, 852
NM62, 853
NM64, 854
NM83, 855
NRREF, 856
NSAO, 857
NSAQ, 858
NSAQR, 859
NSC2A, 860
NSC2S, 861
NSC2Z, 862
NSDAT, 863
NSDS, 864
NSE, 865
NSEAI, 866
NSLE, 867
NSLIL, 868
NSNM, 869
NSR, 870
NSS, 871
OLTTR, 872
ONFV, 873
ONTV, 874
OSGMD, 875
OSMC, 876
PCVS, 877
PM, 878
PSHS, 879
PTM, 880
PTMEE, 881
RAO, 882
RES, 883
RNM, 884
RNSM, 885
ROD2, 886
ROD4, 887
RREF, 888
RREFN, 889
RRTI, 890
RS, 891
RSAI, 892
RSB, 893
RSC5, 894
RSNS, 895
RSREM, 896
RSSC4, 897
RVMR, 898
S, 899
SAA, 900
SAB, 901
SABMI, 902
SAE, 903
SAN, 904
SAR, 905
SAV, 906
SC, 907
SC3, 908
SCAA, 909
SCAB, 910
SCAD, 911
SDS, 912
SEE, 913
SEEF, 914
SETM, 915
SI, 916
SM2Z7, 917
SM32, 918
SMLT, 919
SMS3, 920
SMS5, 921
SP4, 922
SPIAS, 923
SRR, 924
SS, 925
SSC, 926
SSET, 927
SSM22, 928
SSNS, 929
SSP, 930
SSP4, 931
STLT, 932
STNE, 933
SU, 934
SUVOS, 935
SVP4, 936
SYM, 937
TCSD, 938
TD4, 939
TDEE6, 940
TDSSE, 941
TIS, 942
TIVS, 943
TKAP, 944
TLC, 945
TM, 946
TMP, 947
TOV, 948
TREM, 949
TTS, 950
UM3, 951
UPM, 952
US, 953
USR, 954
VA, 955
VESE, 956
VFS, 957
VFSAD, 958
VFSAI, 959
VFSAL, 960
VRC4, 961
VRP2, 962
VSCV, 963
VSF, 964
VSIM5, 965
VSIS, 966
VSM, 967
VSP, 968
VSPUD, 969
VSS, 970
ZNDAB, 971
EXC (subsection, section B), 972
EXC (subsection, section CB), 973
EXC (subsection, section CRS), 974
EXC (subsection, section D), 975
EXC (subsection, section DM), 976
EXC (subsection, section EE), 977
EXC (subsection, section F), 978
EXC (subsection, section FS), 979
EXC (subsection, section HSE), 980
EXC (subsection, section ILT), 981
EXC (subsection, section IVLT), 982
EXC (subsection, section LC), 983
EXC (subsection, section LDS), 984
EXC (subsection, section LI), 985
EXC (subsection, section LISS), 986
EXC (subsection, section LT), 987
EXC (subsection, section MINM), 988
EXC (subsection, section MISLE), 989
EXC (subsection, section MM), 990
EXC (subsection, section MO), 991
EXC (subsection, section MR), 992
EXC (subsection, section NM), 993
EXC (subsection, section O), 994
EXC (subsection, section PD), 995
EXC (subsection, section PDM), 996
EXC (subsection, section PEE), 997
EXC (subsection, section RREF), 998
EXC (subsection, section S), 999
EXC (subsection, section SD), 1000
EXC (subsection, section SLT), 1001
EXC (subsection, section SS), 1002
EXC (subsection, section SSLE), 1003
EXC (subsection, section TSS), 1004
EXC (subsection, section VO), 1005
EXC (subsection, section VR), 1006
EXC (subsection, section VS), 1007
EXC (subsection, section WILA), 1008
extended echelon form
submatrices
example SEEF, 1009
extended reduced row-echelon form
properties
theorem PEEF, 1010
F (archetype), 1011
F (definition), 1012
F (section), 1013
F (subsection, section F), 1014
FDV (example), 1015
FF (subsection, section F), 1016
FF8 (example), 1017
field
definition F, 1018
FIMP (theorem), 1019
finite field
size 8
example FF8, 1020
four subsets
example FS1, 1021
example FS2, 1022
four subspaces
dimension
theorem DFS, 1023
FRAN (example), 1024
free variables
example CFV, 1025
free variables, number
theorem FVCS, 1026
free, independent variables
example FDV, 1027
FS (section), 1028
FS (subsection, section FS), 1029
FS (theorem), 1030
FS1 (example), 1031
FS2 (example), 1032
FSAG (example), 1033
FTMR (theorem), 1034
FV (subsection, section TSS), 1035
FVCS (theorem), 1036
G (archetype), 1037
G (theorem), 1038
GE4 (example), 1039
GE6 (example), 1040
GEE (subsection, section IS), 1041
GEK (theorem), 1042
generalized eigenspace
as kernel
theorem GEK, 1043
definition GES, 1044
dimension
theorem DGES, 1045
dimension 4 domain
example GE4, 1046
dimension 6 domain
example GE6, 1047
invariant subspace
theorem GESIS, 1048
nilpotent restriction
theorem RGEN, 1049
nilpotent restrictions, dimension 6 domain
example GENR6, 1050
notation, 1051
generalized eigenspace decomposition
theorem GESD, 1052
generalized eigenvector
definition GEV, 1053
GENR6 (example), 1054
GES (definition), 1055
GES (notation), 1056
GESD (subsection, section JCF), 1057
GESD (theorem), 1058
GESIS (theorem), 1059
GEV (definition), 1060
GFDL (appendix), 1061
GME (definition), 1062
goldilocks
theorem G, 1063
Gram-Schmidt
column vectors
theorem GSPCV, 1064
three vectors
example GSTV, 1065
gram-schmidt
mathematica, 1066
GS (technique, section PT), 1067
GSP (subsection, section O), 1068
GSP.MMA (computation, section MMA), 1069
GSPCV (theorem), 1070
GSTV (example), 1071
GT (subsection, section PD), 1072
H (archetype), 1073
hermitian
definition HM, 1074
HISAA (example), 1075
HISAD (example), 1076
HM (definition), 1077
HMEM5 (example), 1078
HMOE (theorem), 1079
HMRE (theorem), 1080
HMVEI (theorem), 1081
homogeneous system
consistent
theorem HSC, 1082
definition HS, 1083
infinitely many solutions
theorem HMVEI, 1084
homogeneous systems
linear independence, 1085
homogenous system
Archetype C
example AHSAC, 1086
HPDM (example), 1087
HS (definition), 1088
HSC (theorem), 1089
HSE (section), 1090
HUSAB (example), 1091
I (archetype), 1092
I (technique, section PT), 1093
IAP (example), 1094
IAR (example), 1095
IAS (example), 1096
IAV (example), 1097
ICBM (theorem), 1098
ICLT (theorem), 1099
identities
technique PI, 1100
identity matrix
determinant, 1101
example IM, 1102
notation, 1103
IDLT (definition), 1104
IDV (definition), 1105
IE (definition), 1106
IE (notation), 1107
IFDVS (theorem), 1108
IILT (theorem), 1109
ILT (definition), 1110
ILT (section), 1111
ILTB (theorem), 1112
ILTD (subsection, section ILT), 1113
ILTD (theorem), 1114
ILTIS (theorem), 1115
ILTLI (subsection, section ILT), 1116
ILTLI (theorem), 1117
ILTLT (theorem), 1118
ILTVR (example), 1119
IM (definition), 1120
IM (example), 1121
IM (notation), 1122
IM (subsection, section MISLE), 1123
IM11 (example), 1124
IMILT (theorem), 1125
IMP (definition), 1126
IMR (theorem), 1127
inconsistent linear systems
theorem ISRN, 1128
independent, dependent variables
definition IDV, 1129
indesxstring
example SM2Z7, 1130
example SSET, 1131
index
eigenvalue
definition IE, 1132
notation, 1133
indexstring
theorem DRCMA, 1134
theorem OBUTR, 1135
induction
technique I, 1136
infinite solution set
example ISSI, 1137
infinite solutions,
example IS, 1138
injective
example IAP, 1139
example IAR, 1140
not
example NIAO, 1141
example NIAQ, 1142
example NIAQR, 1143
not, by dimension
example NIDAU, 1144
polynomials to matrices
example IAV, 1145
injective linear transformation
bases
theorem ILTB, 1146
injective linear transformations
dimension
theorem ILTD, 1147
inner product
anti-commutative
theorem IPAC, 1148
example CSIP, 1149
norm
theorem IPN, 1150
notation, 1151
positive
theorem PIP, 1152
scalar multiplication
theorem IPSM, 1153
vector addition
theorem IPVA, 1154
integers
mod
definition IMP, 1155
mod ,
field
theorem FIMP, 1156
mod 11
example IM11, 1157
invariant subspace
definition IS, 1158
eigenspace, 1159
eigenspaces
example EIS, 1160
example TIS, 1161
Jordan block
example ISJB, 1162
kernels of powers
theorem KPIS, 1163
inverse
composition of linear transformations
theorem ICLT, 1164
example CMI, 1165
example MI, 1166
notation, 1167
of a matrix, 1168
invertible linear transformation
defined by invertible matrix
theorem IMILT, 1169
invertible linear transformations
composition
theorem CIVLT, 1170
IP (definition), 1171
IP (notation), 1172
IP (subsection, section O), 1173
IPAC (theorem), 1174
IPN (theorem), 1175
IPSM (theorem), 1176
IPVA (theorem), 1177
IS (definition), 1178
IS (example), 1179
IS (section), 1180
IS (subsection, section IS), 1181
ISJB (example), 1182
ISMR4 (example), 1183
ISMR6 (example), 1184
isomorphic
multiple vector spaces
example MIVS, 1185
vector spaces
example IVSAV, 1186
isomorphic vector spaces
dimension
theorem IVSED, 1187
example TIVS, 1188
ISRN (theorem), 1189
ISSI (example), 1190
ITMT (theorem), 1191
IV (subsection, section IVLT), 1192
IVLT (definition), 1193
IVLT (section), 1194
IVLT (subsection, section IVLT), 1195
IVLT (subsection, section MR), 1196
IVS (definition), 1197
IVSAV (example), 1198
IVSED (theorem), 1199
J (archetype), 1200
JB (definition), 1201
JB (notation), 1202
JB4 (example), 1203
JCF (definition), 1204
JCF (section), 1205
JCF (subsection, section JCF), 1206
JCF10 (example), 1207
JCFLT (theorem), 1208
Jordan block
definition JB, 1209
nilpotent
theorem NJB, 1210
notation, 1211
size 4
example JB4, 1212
Jordan canonical form
definition JCF, 1213
size 10
example JCF10, 1214
K (archetype), 1215
kernel
injective linear transformation
theorem KILT, 1216
isomorphic to null space
theorem KNSI, 1217
linear transformation
example NKAO, 1218
notation, 1219
of a linear transformation
definition KLT, 1220
pre-image, 1221
subspace
theorem KLTS, 1222
trivial
example TKAP, 1223
via matrix representation
example KVMR, 1224
KILT (theorem), 1225
KLT (definition), 1226
KLT (notation), 1227
KLT (subsection, section ILT), 1228
KLTS (theorem), 1229
KNSI (theorem), 1230
KPI (theorem), 1231
KPIS (theorem), 1232
KPLT (theorem), 1233
KPNLT (example), 1234
KPNLT (theorem), 1235
KVMR (example), 1236
L (archetype), 1237
L (technique, section PT), 1238
LA (subsection, section WILA), 1239
LC (definition), 1240
LC (section), 1241
LC (subsection, section LC), 1242
LC (technique, section PT), 1243
LCCV (definition), 1244
LCM (example), 1245
LDCAA (example), 1246
LDHS (example), 1247
LDP4 (example), 1248
LDRN (example), 1249
LDS (example), 1250
LDS (section), 1251
LDSS (subsection, section LDS), 1252
left null space
as row space, 1253
definition LNS, 1254
example LNS, 1255
notation, 1256
subspace
theorem LNSMS, 1257
lemma
technique LC, 1258
LI (definition), 1259
LI (section), 1260
LI (subsection, section LISS), 1261
LIC (example), 1262
LICAB (example), 1263
LICV (definition), 1264
LIHS (example), 1265
LIM32 (example), 1266
linear combination
system of equations
example ABLC, 1267
definition LC, 1268
definition LCCV, 1269
example TLC, 1270
linear transformation, 1271
matrices
example LCM, 1272
system of equations
example AALC, 1273
linear combinations
solutions to linear systems
theorem SLSLC, 1274
linear dependence
more vectors than size
theorem MVSLD, 1275
linear independence
definition LI, 1276
definition LICV, 1277
homogeneous systems
theorem LIVHS, 1278
injective linear transformation
theorem ILTLI, 1279
matrices
example LIM32, 1280
orthogonal, 1281
r and n
theorem LIVRN, 1282
linear solve
mathematica, 1283
linear system
consistent
theorem RCLS, 1284
matrix representation
definition LSMR, 1285
notation, 1286
linear systems
notation
example MNSLE, 1287
example NSLE, 1288
linear transformation
polynomials to polynomials
example LTPP, 1289
addition
definition LTA, 1290
theorem MLTLT, 1291
theorem SLTLT, 1292
as matrix multiplication
example ALTMM, 1293
basis of range
example BRLT, 1294
checking
example ALT, 1295
composition
definition LTC, 1296
theorem CLTLT, 1297
defined by a matrix
example LTM, 1298
defined on a basis
example LTDB1, 1299
example LTDB2, 1300
example LTDB3, 1301
theorem LTDB, 1302
definition LT, 1303
identity
definition IDLT, 1304
injection
definition ILT, 1305
inverse
theorem ILTLT, 1306
inverse of inverse
theorem IILT, 1307
invertible
definition IVLT, 1308
example AIVLT, 1309
invertible, injective and surjective
theorem ILTIS, 1310
Jordan canonical form
theorem JCFLT, 1311
kernels of powers
theorem KPLT, 1312
linear combination
theorem LTLC, 1313
matrix of, 1314
example MFLT, 1315
example MOLT, 1316
not
example NLT, 1317
not invertible
example ANILT, 1318
notation, 1319
polynomials to matrices
example LTPM, 1320
rank plus nullity
theorem RPNDD, 1321
restriction
definition LTR, 1322
notation, 1323
scalar multiple
example SMLT, 1324
scalar multiplication
definition LTSM, 1325
spanning range
theorem SSRLT, 1326
sum
example STLT, 1327
surjection
definition SLT, 1328
vector space of, 1329
zero vector
theorem LTTZZ, 1330
linear transformation inverse
via matrix representation
example ILTVR, 1331
linear transformation restriction
on generalized eigenspace
example LTRGE, 1332
linear transformations
compositions
example CTLT, 1333
from matrices
theorem MBLT, 1334
linearly dependent
example LDRN, 1335
via homogeneous system
example LDHS, 1336
linearly dependent columns
Archetype A
example LDCAA, 1337
linearly dependent set
example LDS, 1338
linear combinations within
theorem DLDS, 1339
polynomials
example LDP4, 1340
linearly independent
crazy vector space
example LIC, 1341
extending sets
theorem ELIS, 1342
polynomials
example LIP4, 1343
via homogeneous system
example LIHS, 1344
linearly independent columns
Archetype B
example LICAB, 1345
linearly independent set
example LIS, 1346
example LLDS, 1347
LINM (subsection, section LI), 1348
LINSB (example), 1349
LIP4 (example), 1350
LIS (example), 1351
LISS (section), 1352
LISV (subsection, section LI), 1353
LIVHS (theorem), 1354
LIVRN (theorem), 1355
LLDS (example), 1356
LNS (definition), 1357
LNS (example), 1358
LNS (notation), 1359
LNS (subsection, section FS), 1360
LNSMS (theorem), 1361
lower triangular matrix
definition LTM, 1362
LS.MMA (computation, section MMA), 1363
LSMR (definition), 1364
LSMR (notation), 1365
LT (chapter), 1366
LT (definition), 1367
LT (notation), 1368
LT (section), 1369
LT (subsection, section LT), 1370
LTA (definition), 1371
LTC (definition), 1372
LTDB (theorem), 1373
LTDB1 (example), 1374
LTDB2 (example), 1375
LTDB3 (example), 1376
LTLC (subsection, section LT), 1377
LTLC (theorem), 1378
LTM (definition), 1379
LTM (example), 1380
LTPM (example), 1381
LTPP (example), 1382
LTR (definition), 1383
LTR (notation), 1384
LTRGE (example), 1385
LTSM (definition), 1386
LTTZZ (theorem), 1387
M (archetype), 1388
M (chapter), 1389
M (definition), 1390
M (notation), 1391
MA (definition), 1392
MA (example), 1393
MA (notation), 1394
MACN (Property), 1395
MAF (Property), 1396
mathematica
gram-schmidt (computation), 1397
linear solve (computation), 1398
matrix entry (computation), 1399
matrix inverse (computation), 1400
matrix multiplication (computation), 1401
null space (computation), 1402
row reduce (computation), 1403
transpose of a matrix (computation), 1404
vector form of solutions (computation), 1405
vector linear combinations (computation), 1406
mathematical language
technique L, 1407
matrix
addition
definition MA, 1408
notation, 1409
augmented
definition AM, 1410
column space
definition CSM, 1411
complex conjugate
example CCM, 1412
definition M, 1413
equality
definition ME, 1414
notation, 1415
example AM, 1416
identity
definition IM, 1417
inverse
definition MI, 1418
nonsingular
definition NM, 1419
notation, 1420
of a linear transformation
theorem MLTCV, 1421
product
example PTM, 1422
example PTMEE, 1423
product with vector
definition MVP, 1424
rectangular, 1425
row space
definition RSM, 1426
scalar multiplication
definition MSM, 1427
notation, 1428
singular, 1429
square
definition SQM, 1430
submatrices
example SS, 1431
submatrix
definition SM, 1432
symmetric
definition SYM, 1433
transpose
definition TM, 1434
unitary
definition UM, 1435
unitary is invertible
theorem UMI, 1436
zero
definition ZM, 1437
matrix addition
example MA, 1438
matrix components
notation, 1439
matrix entry
mathematica, 1440
ti83, 1441
ti86, 1442
matrix inverse
Archetype B, 1443
computation
theorem CINM, 1444
mathematica, 1445
nonsingular matrix
theorem NI, 1446
of a matrix inverse
theorem MIMI, 1447
one-sided
theorem OSIS, 1448
product
theorem SS, 1449
scalar multiple
theorem MISM, 1450
size 2 matrices
theorem TTMI, 1451
transpose
theorem MIT, 1452
uniqueness
theorem MIU, 1453
matrix multiplication
associativity
theorem MMA, 1454
complex conjugation
theorem MMCC, 1455
definition MM, 1456
distributivity
theorem MMDAA, 1457
entry-by-entry
theorem EMP, 1458
identity matrix
theorem MMIM, 1459
inner product
theorem MMIP, 1460
mathematica, 1461
noncommutative
example MMNC, 1462
scalar matrix multiplication
theorem MMSMM, 1463
systems of linear equations
theorem SLEMM, 1464
transposes
theorem MMT, 1465
zero matrix
theorem MMZM, 1466
matrix product
as composition of linear transformations
example MPMR, 1467
matrix representation
basis of eigenvectors
example MRBE, 1468
composition of linear transformations
theorem MRCLT, 1469
definition MR, 1470
invertible
theorem IMR, 1471
multiple of a linear transformation
theorem MRMLT, 1472
restriction to generalized eigenspace
theorem MRRGE, 1473
sum of linear transformations
theorem MRSLT, 1474
theorem FTMR, 1475
upper triangular
theorem UTMR, 1476, 1477
matrix representations
converting with change-of-basis
example MRCM, 1478
example OLTTR, 1479
matrix scalar multiplication
example MSM, 1480
matrix vector space
dimension
theorem DM, 1481
matrix-vector product
example MTV, 1482
notation, 1483
MBC (example), 1484
MBLT (theorem), 1485
MC (notation), 1486
MCC (subsection, section MO), 1487
MCCN (Property), 1488
MCF (Property), 1489, 1490
MCN (definition), 1491
MCN (subsection, section CNO), 1492
MCSM (example), 1493
MCT (theorem), 1494
MD (chapter), 1495
ME (definition), 1496
ME (notation), 1497
ME (subsection, section PEE), 1498
ME (technique, section PT), 1499
ME (theorem), 1500
ME.MMA (computation, section MMA), 1501
ME.TI83 (computation, section TI83), 1502
ME.TI86 (computation, section TI86), 1503
MEASM (subsection, section MO), 1504
MFLT (example), 1505
MI (definition), 1506
MI (example), 1507
MI (notation), 1508
MI.MMA (computation, section MMA), 1509
MICN (Property), 1510
MIF (Property), 1511
MIMI (theorem), 1512
MINM (section), 1513
MISLE (section), 1514
MISM (theorem), 1515
MIT (theorem), 1516
MIU (theorem), 1517
MIVS (example), 1518
MLT (subsection, section LT), 1519
MLTCV (theorem), 1520
MLTLT (theorem), 1521
MM (definition), 1522
MM (section), 1523
MM (subsection, section MM), 1524
MM.MMA (computation, section MMA), 1525
MMA (section), 1526
MMA (theorem), 1527
MMCC (theorem), 1528
MMDAA (theorem), 1529
MMEE (subsection, section MM), 1530
MMIM (theorem), 1531
MMIP (theorem), 1532
MMNC (example), 1533
MMSMM (theorem), 1534
MMT (theorem), 1535
MMZM (theorem), 1536
MNEM (theorem), 1537
MNSLE (example), 1538
MO (section), 1539
MOLT (example), 1540
more variables than equations
example OSGMD, 1541
theorem CMVEI, 1542
MPMR (example), 1543
MR (definition), 1544
MR (section), 1545
MRBE (example), 1546
MRCB (theorem), 1547
MRCLT (theorem), 1548
MRCM (example), 1549
MRMLT (theorem), 1550
MRRGE (theorem), 1551
MRS (subsection, section CB), 1552
MRSLT (theorem), 1553
MSCN (example), 1554
MSM (definition), 1555
MSM (example), 1556
MSM (notation), 1557
MTV (example), 1558
multiplicative associativity
complex numbers
Property MACN, 1559
multiplicative closure
field
Property MCF, 1560
multiplicative commuativity
complex numbers
Property MCCN, 1561
multiplicative inverse
complex numbers
Property MICN, 1562
MVNSE (subsection, section RREF), 1563
MVP (definition), 1564
MVP (notation), 1565
MVP (subsection, section MM), 1566
MVSLD (theorem), 1567
MWIAA (example), 1568
N (archetype), 1569
N (subsection, section O), 1570
N (technique, section PT), 1571
NDMS4 (example), 1572
negation of statements
technique N, 1573
NEM (theorem), 1574
NI (theorem), 1575
NIAO (example), 1576
NIAQ (example), 1577
NIAQR (example), 1578
NIDAU (example), 1579
nilpotent
linear transformation
definition NLT, 1580
NJB (theorem), 1581
NJB5 (example), 1582
NKAO (example), 1583
NLT (definition), 1584
NLT (example), 1585
NLT (section), 1586
NLT (subsection, section NLT), 1587
NLTFO (subsection, section LT), 1588
NM (definition), 1589
NM (example), 1590
NM (section), 1591
NM (subsection, section NM), 1592
NM (subsection, section OD), 1593
NM62 (example), 1594
NM64 (example), 1595
NM83 (example), 1596
NME1 (theorem), 1597
NME2 (theorem), 1598
NME3 (theorem), 1599
NME4 (theorem), 1600
NME5 (theorem), 1601
NME6 (theorem), 1602
NME7 (theorem), 1603
NME8 (theorem), 1604
NME9 (theorem), 1605
NMI (subsection, section MINM), 1606
NMLIC (theorem), 1607
NMPEM (theorem), 1608
NMRRI (theorem), 1609
NMTNS (theorem), 1610
NMUS (theorem), 1611
NOILT (theorem), 1612
NOLT (definition), 1613
NOLT (notation), 1614
NOM (definition), 1615
NOM (notation), 1616
nonsingular
columns as basis
theorem CNMB, 1617
nonsingular matrices
linearly independent columns
theorem NMLIC, 1618
nonsingular matrix
Archetype B
example NM, 1619
column space, 1620
elemntary matrices
theorem NMPEM, 1621
equivalences
theorem NME1, 1622
theorem NME2, 1623
theorem NME3, 1624
theorem NME4, 1625
theorem NME5, 1626
theorem NME6, 1627
theorem NME7, 1628
theorem NME8, 1629
theorem NME9, 1630
matrix inverse, 1631
null space
example NSNM, 1632
nullity, 1633
product of nonsingular matrices
theorem NPNT, 1634
rank
theorem RNNM, 1635
row-reduced
theorem NMRRI, 1636
trivial null space
theorem NMTNS, 1637
unique solutions
theorem NMUS, 1638
nonsingular matrix, row-reduced
example NSR, 1639
norm
example CNSV, 1640
inner product, 1641
notation, 1642
normal matrix
definition NRML, 1643
example ANM, 1644
notation
A, 1645
AM, 1646
C, 1647
CCCV, 1648
CCM, 1649
CCN, 1650
CNA, 1651
CNE, 1652
CNM, 1653
CSM, 1654
CV, 1655
CVA, 1656
CVC, 1657
CVE, 1658
CVSM, 1659
D, 1660
DM, 1661
DS, 1662
ELEM, 1663
ES, 1664
GES, 1665
IE, 1666
IM, 1667
IP, 1668
JB, 1669
KLT, 1670
LNS, 1671
LSMR, 1672
LT, 1673
LTR, 1674
M, 1675
MA, 1676
MC, 1677
ME, 1678
MI, 1679
MSM, 1680
MVP, 1681
NOLT, 1682
NOM, 1683
NSM, 1684
NV, 1685
RLT, 1686
RO, 1687
ROLT, 1688
ROM, 1689
RREFA, 1690
RSM, 1691
SC, 1692
SE, 1693
SETM, 1694
SI, 1695
SM, 1696
SSET, 1697
SSV, 1698
SU, 1699
TM, 1700
VSCV, 1701
VSM, 1702
ZCV, 1703
ZM, 1704
notation for a linear system
example NSE, 1705
NPNT (theorem), 1706
NRFO (subsection, section MR), 1707
NRML (definition), 1708
NRREF (example), 1709
NS.MMA (computation, section MMA), 1710
NSAO (example), 1711
NSAQ (example), 1712
NSAQR (example), 1713
NSC2A (example), 1714
NSC2S (example), 1715
NSC2Z (example), 1716
NSDAT (example), 1717
NSDS (example), 1718
NSE (example), 1719
NSEAI (example), 1720
NSLE (example), 1721
NSLIL (example), 1722
NSM (definition), 1723
NSM (notation), 1724
NSM (subsection, section HSE), 1725
NSMS (theorem), 1726
NSNM (example), 1727
NSNM (subsection, section NM), 1728
NSR (example), 1729
NSS (example), 1730
NSSLI (subsection, section LI), 1731
Null space
as a span
example NSDS, 1732
null space
Archetype I
example NSEAI, 1733
basis
theorem BNS, 1734
computation
example CNS1, 1735
example CNS2, 1736
isomorphic to kernel, 1737
linearly independent basis
example LINSB, 1738
mathematica, 1739
matrix
definition NSM, 1740
nonsingular matrix, 1741
notation, 1742
singular matrix, 1743
spanning set
example SSNS, 1744
theorem SSNS, 1745
subspace
theorem NSMS, 1746
null space span, linearly independent
Archetype L
example NSLIL, 1747
nullity
computing, 1748
injective linear transformation
theorem NOILT, 1749
linear transformation
definition NOLT, 1750
matrix, 1751
definition NOM, 1752
notation, 1753, 1754
square matrix, 1755
NV (definition), 1756
NV (notation), 1757
O (archetype), 1758
O (Property), 1759
O (section), 1760
OBC (subsection, section B), 1761
OBUTR (theorem), 1762
OC (Property), 1763
OCN (Property), 1764
OD (section), 1765
OD (subsection, section OD), 1766
OD (theorem), 1767
OF (Property), 1768
OLTTR (example), 1769
OM (Property), 1770
one
column vectors
Property OC, 1771
complex numbers
Property OCN, 1772
field
Property OF, 1773
matrices
Property OM, 1774
vectors
Property O, 1775
ONFV (example), 1776
ONS (definition), 1777
ONTV (example), 1778
orthogonal
linear independence
theorem OSLI, 1779
set
example AOS, 1780
set of vectors
definition OSV, 1781
vector pairs
definition OV, 1782
orthogonal vectors
example TOV, 1783
orthonormal
definition ONS, 1784
matrix columns
example OSMC, 1785
orthonormal diagonalization
theorem OD, 1786
orthonormal set
four vectors
example ONFV, 1787
three vectors
example ONTV, 1788
OSGMD (example), 1789
OSIS (theorem), 1790
OSLI (theorem), 1791
OSMC (example), 1792
OSV (definition), 1793
OV (definition), 1794
OV (subsection, section O), 1795
P (appendix), 1796
P (archetype), 1797
P (technique, section PT), 1798
particular solutions
example PSHS, 1799
PCNA (theorem), 1800
PCVS (example), 1801
PD (section), 1802
PDM (section), 1803
PEE (section), 1804
PEEF (theorem), 1805
PI (definition), 1806
PI (subsection, section LT), 1807
PI (technique, section PT), 1808
PIP (theorem), 1809
PM (example), 1810
PM (subsection, section EE), 1811
PMI (subsection, section MISLE), 1812
PMM (subsection, section MM), 1813
PMR (subsection, section MR), 1814
PNLT (subsection, section NLT), 1815
polynomial
of a matrix
example PM, 1816
polynomial vector space
dimension
theorem DP, 1817
practice
technique P, 1818
pre-image
definition PI, 1819
kernel
theorem KPI, 1820
pre-images
example SPIAS, 1821
product of triangular matrices
theorem PTMT, 1822
Property
AA, 1823
AAC, 1824
AACN, 1825
AAF, 1826
AAM, 1827
AC, 1828
ACC, 1829
ACCN, 1830
ACF, 1831, 1832
ACM, 1833
AI, 1834
AIC, 1835
AICN, 1836
AIF, 1837
AIM, 1838
C, 1839
CC, 1840
CM, 1841
DCN, 1842
DF, 1843
DMAM, 1844
DSA, 1845
DSAC, 1846
DSAM, 1847
DVA, 1848
DVAC, 1849
MACN, 1850
MAF, 1851
MCCN, 1852
MCF, 1853, 1854
MICN, 1855
MIF, 1856
O, 1857
OC, 1858
OCN, 1859
OF, 1860
OM, 1861
SC, 1862
SCC, 1863
SCM, 1864
SMA, 1865
SMAC, 1866
SMAM, 1867
Z, 1868
ZC, 1869
ZCN, 1870
ZF, 1871
ZM, 1872
PSHS (example), 1873
PSHS (subsection, section LC), 1874
PSM (subsection, section SD), 1875
PSPHS (theorem), 1876
PSS (subsection, section SSLE), 1877
PSSD (theorem), 1878
PSSLS (theorem), 1879
PT (section), 1880
PTM (example), 1881
PTMEE (example), 1882
PTMT (theorem), 1883
Q (archetype), 1884
R (archetype), 1885
R (chapter), 1886
range
full
example FRAN, 1887
isomorphic to column space
theorem RCSI, 1888
linear transformation
example RAO, 1889
notation, 1890
of a linear transformation
definition RLT, 1891
pre-image
theorem RPI, 1892
subspace
theorem RLTS, 1893
surjective linear transformation
theorem RSLT, 1894
via matrix representation
example RVMR, 1895
rank
computing
theorem CRN, 1896
linear transformation
definition ROLT, 1897
matrix
definition ROM, 1898
example RNM, 1899
notation, 1900, 1901
of transpose
example RRTI, 1902
square matrix
example RNSM, 1903
surjective linear transformation
theorem ROSLT, 1904
transpose
theorem RMRT, 1905
rank one decomposition
size 2
example ROD2, 1906
size 4
example ROD4, 1907
theorem ROD, 1908
rank+nullity
theorem RPNC, 1909
RAO (example), 1910
RCLS (theorem), 1911
RCSI (theorem), 1912
RD (subsection, section VS), 1913
RDS (theorem), 1914
READ (subsection, section B), 1915
READ (subsection, section CB), 1916
READ (subsection, section CRS), 1917
READ (subsection, section D), 1918
READ (subsection, section DM), 1919
READ (subsection, section EE), 1920
READ (subsection, section FS), 1921
READ (subsection, section HSE), 1922
READ (subsection, section ILT), 1923
READ (subsection, section IVLT), 1924
READ (subsection, section LC), 1925
READ (subsection, section LDS), 1926
READ (subsection, section LI), 1927
READ (subsection, section LISS), 1928
READ (subsection, section LT), 1929
READ (subsection, section MINM), 1930
READ (subsection, section MISLE), 1931
READ (subsection, section MM), 1932
READ (subsection, section MO), 1933
READ (subsection, section MR), 1934
READ (subsection, section NM), 1935
READ (subsection, section O), 1936
READ (subsection, section PD), 1937
READ (subsection, section PDM), 1938
READ (subsection, section PEE), 1939
READ (subsection, section RREF), 1940
READ (subsection, section S), 1941
READ (subsection, section SD), 1942
READ (subsection, section SLT), 1943
READ (subsection, section SS), 1944
READ (subsection, section SSLE), 1945
READ (subsection, section TSS), 1946
READ (subsection, section VO), 1947
READ (subsection, section VR), 1948
READ (subsection, section VS), 1949
READ (subsection, section WILA), 1950
reduced row-echelon form
analysis
notation, 1951
definition RREF, 1952
example NRREF, 1953
example RREF, 1954
extended
definition EEF, 1955
notation
example RREFN, 1956
unique
theorem RREFU, 1957
reducing a span
example RSC5, 1958
relation of linear dependence
definition RLD, 1959
definition RLDCV, 1960
REM (definition), 1961
REMEF (theorem), 1962
REMES (theorem), 1963
REMRS (theorem), 1964
RES (example), 1965
RGEN (theorem), 1966
RLD (definition), 1967
RLDCV (definition), 1968
RLT (definition), 1969
RLT (notation), 1970
RLT (subsection, section IS), 1971
RLT (subsection, section SLT), 1972
RLTS (theorem), 1973
RMRT (theorem), 1974
RNLT (subsection, section IVLT), 1975
RNM (example), 1976
RNM (subsection, section D), 1977
RNNM (subsection, section D), 1978
RNNM (theorem), 1979
RNSM (example), 1980
RO (definition), 1981
RO (notation), 1982
RO (subsection, section RREF), 1983
ROD (section), 1984
ROD (theorem), 1985
ROD2 (example), 1986
ROD4 (example), 1987
ROLT (definition), 1988
ROLT (notation), 1989
ROM (definition), 1990
ROM (notation), 1991
ROSLT (theorem), 1992
row operations
definition RO, 1993
elementary matrices, 1994, 1995
notation, 1996
row reduce
mathematica, 1997
ti83, 1998
ti86, 1999
row space
Archetype I
example RSAI, 2000
as column space, 2001
basis
example RSB, 2002
theorem BRS, 2003
matrix, 2004
notation, 2005
row-equivalent matrices
theorem REMRS, 2006
subspace
theorem RSMS, 2007
row-equivalent matrices
definition REM, 2008
example TREM, 2009
row space, 2010
row spaces
example RSREM, 2011
theorem REMES, 2012
row-reduce
the verb
definition RR, 2013
row-reduced matrices
theorem REMEF, 2014
RPI (theorem), 2015
RPNC (theorem), 2016
RPNDD (theorem), 2017
RR (definition), 2018
RR.MMA (computation, section MMA), 2019
RR.TI83 (computation, section TI83), 2020
RR.TI86 (computation, section TI86), 2021
RREF (definition), 2022
RREF (example), 2023
RREF (section), 2024
RREF (subsection, section RREF), 2025
RREFA (notation), 2026
RREFN (example), 2027
RREFU (theorem), 2028
RRTI (example), 2029
RS (example), 2030
RSAI (example), 2031
RSB (example), 2032
RSC5 (example), 2033
RSLT (theorem), 2034
RSM (definition), 2035
RSM (notation), 2036
RSM (subsection, section CRS), 2037
RSMS (theorem), 2038
RSNS (example), 2039
RSREM (example), 2040
RSSC4 (example), 2041
RT (subsection, section PD), 2042
RVMR (example), 2043
S (archetype), 2044
S (definition), 2045
S (example), 2046
S (section), 2047
SAA (example), 2048
SAB (example), 2049
SABMI (example), 2050
SAE (example), 2051
SAN (example), 2052
SAR (example), 2053
SAV (example), 2054
SC (definition), 2055
SC (example), 2056
SC (notation), 2057
SC (Property), 2058
SC (subsection, section S), 2059
SC (subsection, section SET), 2060
SC3 (example), 2061
SCAA (example), 2062
SCAB (example), 2063
SCAD (example), 2064
scalar closure
column vectors
Property SCC, 2065
matrices
Property SCM, 2066
vectors
Property SC, 2067
scalar multiple
matrix inverse, 2068
scalar multiplication
canceling scalars
theorem CSSM, 2069
canceling vectors
theorem CVSM, 2070
zero scalar
theorem ZSSM, 2071
zero vector
theorem ZVSM, 2072
zero vector result
theorem SMEZV, 2073
scalar multiplication associativity
column vectors
Property SMAC, 2074
matrices
Property SMAM, 2075
vectors
Property SMA, 2076
SCB (theorem), 2077
SCC (Property), 2078
SCM (Property), 2079
SD (section), 2080
SDS (example), 2081
SE (definition), 2082
SE (notation), 2083
SEE (example), 2084
SEEF (example), 2085
SER (theorem), 2086
set
cardinality
definition C, 2087
example CS, 2088
notation, 2089
complement
definition SC, 2090
example SC, 2091
notation, 2092
definition SET, 2093
empty
definition ES, 2094
equality
definition SE, 2095
notation, 2096
intersection
definition SI, 2097
example SI, 2098
notation, 2099
membership
example SETM, 2100
notation, 2101
size, 2102
subset, 2103
union
definition SU, 2104
example SU, 2105
notation, 2106
SET (definition), 2107
SET (section), 2108
SETM (example), 2109
SETM (notation), 2110
shoes, 2111
SHS (subsection, section HSE), 2112
SI (definition), 2113
SI (example), 2114
SI (notation), 2115
SI (subsection, section IVLT), 2116
SIM (definition), 2117
similar matrices
equal eigenvalues
example EENS, 2118
eual eigenvalues
theorem SMEE, 2119
example SMS3, 2120
example SMS5, 2121
similarity
definition SIM, 2122
equivalence relation
theorem SER, 2123
singular matrix
Archetype A
example S, 2124
null space
example NSS, 2125
singular matrix, row-reduced
example SRR, 2126
SLE (chapter), 2127
SLE (definition), 2128
SLE (subsection, section SSLE), 2129
SLELT (subsection, section IVLT), 2130
SLEMM (theorem), 2131
SLSLC (theorem), 2132
SLT (definition), 2133
SLT (section), 2134
SLTB (theorem), 2135
SLTD (subsection, section SLT), 2136
SLTD (theorem), 2137
SLTLT (theorem), 2138
SM (definition), 2139
SM (notation), 2140
SM (subsection, section SD), 2141
SM2Z7 (example), 2142
SM32 (example), 2143
SMA (Property), 2144
SMAC (Property), 2145
SMAM (Property), 2146
SMEE (theorem), 2147
SMEZV (theorem), 2148
SMLT (example), 2149
SMS (theorem), 2150
SMS3 (example), 2151
SMS5 (example), 2152
SMZD (theorem), 2153
SMZE (theorem), 2154
SNCM (theorem), 2155
SO (subsection, section SET), 2156
socks, 2157
SOL (subsection, section B), 2158
SOL (subsection, section CB), 2159
SOL (subsection, section CRS), 2160
SOL (subsection, section D), 2161
SOL (subsection, section DM), 2162
SOL (subsection, section EE), 2163
SOL (subsection, section F), 2164
SOL (subsection, section FS), 2165
SOL (subsection, section HSE), 2166
SOL (subsection, section ILT), 2167
SOL (subsection, section IVLT), 2168
SOL (subsection, section LC), 2169
SOL (subsection, section LDS), 2170
SOL (subsection, section LI), 2171
SOL (subsection, section LISS), 2172
SOL (subsection, section LT), 2173
SOL (subsection, section MINM), 2174
SOL (subsection, section MISLE), 2175
SOL (subsection, section MM), 2176
SOL (subsection, section MO), 2177
SOL (subsection, section MR), 2178
SOL (subsection, section NM), 2179
SOL (subsection, section PD), 2180
SOL (subsection, section PDM), 2181
SOL (subsection, section PEE), 2182
SOL (subsection, section RREF), 2183
SOL (subsection, section S), 2184
SOL (subsection, section SD), 2185
SOL (subsection, section SLT), 2186
SOL (subsection, section SS), 2187
SOL (subsection, section SSLE), 2188
SOL (subsection, section TSS), 2189
SOL (subsection, section VO), 2190
SOL (subsection, section VR), 2191
SOL (subsection, section WILA), 2192
solution set
Archetype A
example SAA, 2193
archetype E
example SAE, 2194
theorem PSPHS, 2195
solution sets
possibilities
theorem PSSLS, 2196
solution vector
definition SV, 2197
solving homogeneous system
Archetype A
example HISAA, 2198
Archetype B
example HUSAB, 2199
Archetype D
example HISAD, 2200
solving nonlinear equations
example STNE, 2201
SP4 (example), 2202
span
basic
example ABS, 2203
basis
theorem BS, 2204
definition SS, 2205
definition SSCV, 2206
improved
example IAS, 2207
notation, 2208
reducing
example RSSC4, 2209
reduction
example RS, 2210
removing vectors
example COV, 2211
reworking elements
example RES, 2212
set of polynomials
example SSP, 2213
subspace
theorem SSS, 2214
span of columns
Archetype A
example SCAA, 2215
Archetype B
example SCAB, 2216
Archetype D
example SCAD, 2217
spanning set
crazy vector space
example SSC, 2218
definition TSVS, 2219
matrices
example SSM22, 2220
more vectors
theorem SSLD, 2221
polynomials
example SSP4, 2222
SPIAS (example), 2223
SQM (definition), 2224
SRR (example), 2225
SS (definition), 2226
SS (example), 2227
SS (section), 2228
SS (subsection, section LISS), 2229
SS (theorem), 2230
SSC (example), 2231
SSCV (definition), 2232
SSET (definition), 2233
SSET (example), 2234
SSET (notation), 2235
SSLD (theorem), 2236
SSLE (section), 2237
SSM22 (example), 2238
SSNS (example), 2239
SSNS (subsection, section SS), 2240
SSNS (theorem), 2241
SSP (example), 2242
SSP4 (example), 2243
SSRLT (theorem), 2244
SSS (theorem), 2245
SSSLT (subsection, section SLT), 2246
SSV (notation), 2247
SSV (subsection, section SS), 2248
starting proofs
technique GS, 2249
STLT (example), 2250
STNE (example), 2251
SU (definition), 2252
SU (example), 2253
SU (notation), 2254
submatrix
notation, 2255
subset
definition SSET, 2256
notation, 2257
subspace
as null space
example RSNS, 2258
characterized
example ASC, 2259
definition S, 2260
in
example SP4, 2261
not, additive closure
example NSC2A, 2262
not, scalar closure
example NSC2S, 2263
not, zero vector
example NSC2Z, 2264
testing
theorem TSS, 2265
trivial
definition TS, 2266
verification
example SC3, 2267
example SM32, 2268
subspaces
equal dimension
theorem EDYES, 2269
surjective
Archetype N
example SAN, 2270
example SAR, 2271
not
example NSAQ, 2272
example NSAQR, 2273
not, Archetype O
example NSAO, 2274
not, by dimension
example NSDAT, 2275
polynomials to matrices
example SAV, 2276
surjective linear transformation
bases
theorem SLTB, 2277
surjective linear transformations
dimension
theorem SLTD, 2278
SUV (definition), 2279
SUVB (theorem), 2280
SUVOS (example), 2281
SV (definition), 2282
SVP4 (example), 2283
SYM (definition), 2284
SYM (example), 2285
symmetric matrices
theorem SMS, 2286
symmetric matrix
example SYM, 2287
system of equations
vector equality
example VESE, 2288
system of linear equations
definition SLE, 2289
T (archetype), 2290
T (part), 2291
T (technique, section PT), 2292
TCSD (example), 2293
TD (section), 2294
TD (subsection, section TD), 2295
TD (theorem), 2296
TD4 (example), 2297
TDEE (theorem), 2298
TDEE6 (example), 2299
TDSSE (example), 2300
TDSSE (subsection, section TD), 2301
technique
C, 2302
CD, 2303
CP, 2304
CV, 2305
D, 2306
DC, 2307
E, 2308
GS, 2309
I, 2310
L, 2311
LC, 2312
ME, 2313
N, 2314
P, 2315
PI, 2316
T, 2317
U, 2318
theorem
AISM, 2319
AIU, 2320
BCS, 2321
BIS, 2322
BNS, 2323
BRS, 2324
BS, 2325
CB, 2326
CCRA, 2327
CCRM, 2328
CCT, 2329
CFDVS, 2330
CFNLT, 2331
CHT, 2332
CILTI, 2333
CINM, 2334
CIVLT, 2335
CLI, 2336
CLTLT, 2337
CMVEI, 2338
CNMB, 2339
COB, 2340
CRMA, 2341
CRMSM, 2342
CRN, 2343
CRSM, 2344
CRVA, 2345
CSCS, 2346
CSLTS, 2347
CSMS, 2348
CSNM, 2349
CSRN, 2350
CSRST, 2351
CSS, 2352
CSSM, 2353
CUMOS, 2354
CVSM, 2355
DC, 2356
DCM, 2357
DCP, 2358
DEC, 2359
DED, 2360
DEM, 2361
DEMMM, 2362
DER, 2363
DERC, 2364
DFS, 2365
DGES, 2366
DIM, 2367
DLDS, 2368
DM, 2369
DMFE, 2370
DMST, 2371
DNLT, 2372
DP, 2373
DRCM, 2374
DRCMA, 2375
DRCS, 2376
DRMM, 2377
DSD, 2378
DSFB, 2379
DSFOS, 2380
DSLI, 2381
DSZI, 2382
DSZV, 2383
DT, 2384
DZRC, 2385
EDELI, 2386
EDYES, 2387
EER, 2388
EIM, 2389
EIS, 2390
ELIS, 2391
EMDRO, 2392
EMHE, 2393
EMMVP, 2394
EMN, 2395
EMNS, 2396
EMP, 2397
EMRCP, 2398
EMS, 2399
ENLT, 2400
EOMP, 2401
EOPSS, 2402
EPM, 2403
ERMCP, 2404
ESMM, 2405
ETM, 2406
FIMP, 2407
FS, 2408
FTMR, 2409
FVCS, 2410
G, 2411
GEK, 2412
GESD, 2413
GESIS, 2414
GSPCV, 2415
HMOE, 2416
HMRE, 2417
HMVEI, 2418
HSC, 2419
ICBM, 2420
ICLT, 2421
IFDVS, 2422
IILT, 2423
ILTB, 2424
ILTD, 2425
ILTIS, 2426
ILTLI, 2427
ILTLT, 2428
IMILT, 2429
IMR, 2430
IPAC, 2431
IPN, 2432
IPSM, 2433
IPVA, 2434
ISRN, 2435
ITMT, 2436
IVSED, 2437
JCFLT, 2438
KILT, 2439
KLTS, 2440
KNSI, 2441
KPI, 2442
KPIS, 2443
KPLT, 2444
KPNLT, 2445
LIVHS, 2446
LIVRN, 2447
LNSMS, 2448
LTDB, 2449
LTLC, 2450
LTTZZ, 2451
MBLT, 2452
MCT, 2453
ME, 2454
MIMI, 2455
MISM, 2456
MIT, 2457
MIU, 2458
MLTCV, 2459
MLTLT, 2460
MMA, 2461
MMCC, 2462
MMDAA, 2463
MMIM, 2464
MMIP, 2465
MMSMM, 2466
MMT, 2467
MMZM, 2468
MNEM, 2469
MRCB, 2470
MRCLT, 2471
MRMLT, 2472
MRRGE, 2473
MRSLT, 2474
MVSLD, 2475
NEM, 2476
NI, 2477
NJB, 2478
NME1, 2479
NME2, 2480
NME3, 2481
NME4, 2482
NME5, 2483
NME6, 2484
NME7, 2485
NME8, 2486
NME9, 2487
NMLIC, 2488
NMPEM, 2489
NMRRI, 2490
NMTNS, 2491
NMUS, 2492
NOILT, 2493
NPNT, 2494
NSMS, 2495
OBUTR, 2496
OD, 2497
OSIS, 2498
OSLI, 2499
PCNA, 2500
PEEF, 2501
PIP, 2502
PSPHS, 2503
PSSD, 2504
PSSLS, 2505
PTMT, 2506
RCLS, 2507
RCSI, 2508
RDS, 2509
REMEF, 2510
REMES, 2511
REMRS, 2512
RGEN, 2513
RLTS, 2514
RMRT, 2515
RNNM, 2516
ROD, 2517
ROSLT, 2518
RPI, 2519
RPNC, 2520
RPNDD, 2521
RREFU, 2522
RSLT, 2523
RSMS, 2524
SCB, 2525
SER, 2526
SLEMM, 2527
SLSLC, 2528
SLTB, 2529
SLTD, 2530
SLTLT, 2531
SMEE, 2532
SMEZV, 2533
SMS, 2534
SMZD, 2535
SMZE, 2536
SNCM, 2537
SS, 2538
SSLD, 2539
SSNS, 2540
SSRLT, 2541
SSS, 2542
SUVB, 2543
TD, 2544
TDEE, 2545
technique T, 2546
TMA, 2547
TMSM, 2548
TSS, 2549
TT, 2550
TTMI, 2551
UMI, 2552
UMPIP, 2553
UTMR, 2554, 2555
VAC, 2556
VFSLS, 2557
VRI, 2558
VRILT, 2559
VRLT, 2560
VRRB, 2561
VRS, 2562
VSLT, 2563
VSPCV, 2564
VSPM, 2565
ZSSM, 2566
ZVSM, 2567
ZVU, 2568
ti83
matrix entry (computation), 2569
row reduce (computation), 2570
vector linear combinations (computation), 2571
TI83 (section), 2572
ti86
matrix entry (computation), 2573
row reduce (computation), 2574
transpose of a matrix (computation), 2575
vector linear combinations (computation), 2576
TI86 (section), 2577
TIS (example), 2578
TIVS (example), 2579
TKAP (example), 2580
TLC (example), 2581
TM (definition), 2582
TM (example), 2583
TM (notation), 2584
TM (subsection, section OD), 2585
TM.MMA (computation, section MMA), 2586
TM.TI86 (computation, section TI86), 2587
TMA (theorem), 2588
TMP (example), 2589
TMSM (theorem), 2590
TOV (example), 2591
trail mix
example TMP, 2592
transpose
matrix scalar multiplication
theorem TMSM, 2593
example TM, 2594
matrix addition
theorem TMA, 2595
matrix inverse, 2596, 2597
notation, 2598
scalar multiplication, 2599
transpose of a matrix
mathematica, 2600
ti86, 2601
transpose of a transpose
theorem TT, 2602
TREM (example), 2603
triangular decomposition
entry by entry, size 6
example TDEE6, 2604
entry by entry
theorem TDEE, 2605
size 4
example TD4, 2606
solving systems of equations
example TDSSE, 2607
theorem TD, 2608
triangular matrix
inverse
theorem ITMT, 2609
trivial solution
system of equations
definition TSHSE, 2610
TS (definition), 2611
TS (subsection, section S), 2612
TSHSE (definition), 2613
TSM (subsection, section MO), 2614
TSS (section), 2615
TSS (subsection, section S), 2616
TSS (theorem), 2617
TSVS (definition), 2618
TT (theorem), 2619
TTMI (theorem), 2620
TTS (example), 2621
typical systems,
example TTS, 2622
U (archetype), 2623
U (technique, section PT), 2624
UM (definition), 2625
UM (subsection, section MINM), 2626
UM3 (example), 2627
UMI (theorem), 2628
UMPIP (theorem), 2629
unique solution,
example US, 2630
example USR, 2631
uniqueness
technique U, 2632
unit vectors
basis
theorem SUVB, 2633
definition SUV, 2634
orthogonal
example SUVOS, 2635
unitary
permutation matrix
example UPM, 2636
size 3
example UM3, 2637
unitary matrices
columns
theorem CUMOS, 2638
unitary matrix
inner product
theorem UMPIP, 2639
UPM (example), 2640
upper triangular matrix
definition UTM, 2641
URREF (subsection, section LC), 2642
US (example), 2643
USR (example), 2644
UTM (definition), 2645
UTMR (subsection, section JCF), 2646
UTMR (subsection, section OD), 2647
UTMR (theorem), 2648, 2649
V (archetype), 2650
V (chapter), 2651
VA (example), 2652
VAC (theorem), 2653
VEASM (subsection, section VO), 2654
vector
addition
definition CVA, 2655
column
definition CV, 2656
equality
definition CVE, 2657
notation, 2658
inner product
definition IP, 2659
norm
definition NV, 2660
notation, 2661
of constants
definition VOC, 2662
product with matrix, 2663, 2664
scalar multiplication
definition CVSM, 2665
vector addition
example VA, 2666
vector component
notation, 2667
vector form of solutions
Archetype D
example VFSAD, 2668
Archetype I
example VFSAI, 2669
Archetype L
example VFSAL, 2670
example VFS, 2671
mathematica, 2672
theorem VFSLS, 2673
vector linear combinations
mathematica, 2674
ti83, 2675
ti86, 2676
vector representation
example AVR, 2677
example VRC4, 2678
injective
theorem VRI, 2679
invertible
theorem VRILT, 2680
linear transformation
definition VR, 2681
theorem VRLT, 2682
surjective
theorem VRS, 2683
theorem VRRB, 2684
vector representations
polynomials
example VRP2, 2685
vector scalar multiplication
example CVSM, 2686
vector space
characterization
theorem CFDVS, 2687
column vectors
definition VSCV, 2688
definition VS, 2689
infinite dimension
example VSPUD, 2690
linear transformations
theorem VSLT, 2691
over integers mod 5
example VSIM5, 2692
vector space of column vectors
notation, 2693
vector space of functions
example VSF, 2694
vector space of infinite sequences
example VSIS, 2695
vector space of matrices
definition VSM, 2696
example VSM, 2697
notation, 2698
vector space of polynomials
example VSP, 2699
vector space properties
column vectors
theorem VSPCV, 2700
matrices
theorem VSPM, 2701
vector space, crazy
example CVS, 2702
vector space, singleton
example VSS, 2703
vector spaces
isomorphic
definition IVS, 2704
theorem IFDVS, 2705
VESE (example), 2706
VFS (example), 2707
VFSAD (example), 2708
VFSAI (example), 2709
VFSAL (example), 2710
VFSLS (theorem), 2711
VFSS (subsection, section LC), 2712
VFSS.MMA (computation, section MMA), 2713
VLC.MMA (computation, section MMA), 2714
VLC.TI83 (computation, section TI83), 2715
VLC.TI86 (computation, section TI86), 2716
VO (section), 2717
VOC (definition), 2718
VR (definition), 2719
VR (section), 2720
VR (subsection, section LISS), 2721
VRC4 (example), 2722
VRI (theorem), 2723
VRILT (theorem), 2724
VRLT (theorem), 2725
VRP2 (example), 2726
VRRB (theorem), 2727
VRS (theorem), 2728
VS (chapter), 2729
VS (definition), 2730
VS (section), 2731
VS (subsection, section VS), 2732
VSCV (definition), 2733
VSCV (example), 2734
VSCV (notation), 2735
VSF (example), 2736
VSIM5 (example), 2737
VSIS (example), 2738
VSLT (theorem), 2739
VSM (definition), 2740
VSM (example), 2741
VSM (notation), 2742
VSP (example), 2743
VSP (subsection, section MO), 2744
VSP (subsection, section VO), 2745
VSP (subsection, section VS), 2746
VSPCV (theorem), 2747
VSPM (theorem), 2748
VSPUD (example), 2749
VSS (example), 2750
W (archetype), 2751
WILA (section), 2752
X (archetype), 2753
Z (Property), 2754
ZC (Property), 2755
ZCN (Property), 2756
ZCV (definition), 2757
ZCV (notation), 2758
zero
complex numbers
Property ZCN, 2759
field
Property ZF, 2760
zero column vector
definition ZCV, 2761
notation, 2762
zero matrix
notation, 2763
zero vector
column vectors
Property ZC, 2764
matrices
Property ZM, 2765
unique
theorem ZVU, 2766
vectors
Property Z, 2767
ZF (Property), 2768
ZM (definition), 2769
ZM (notation), 2770
ZM (Property), 2771
ZNDAB (example), 2772
ZSSM (theorem), 2773
ZVSM (theorem), 2774
ZVU (theorem), 2775