B (archetype), 97
B (definition), 98
B (section), 99
B (subsection, section B), 100
basis
columns nonsingular matrix
example CABAK, 101
common size
theorem BIS, 102
crazy vector apace
example BC, 103
definition B, 104
matrices
example BM, 105
example BSM22, 106
polynomials
example BP, 107
example BPR, 108
example BSP4, 109
example SVP4, 110
subspace of matrices
example BDM22, 111
BC (example), 112
BCS (theorem), 113
BDE (example), 114
BDM22 (example), 115
best cities
money magazine
example MBC, 116
BIS (theorem), 117
BM (example), 118
BNM (subsection, section B), 119
BNS (theorem), 120
BP (example), 121
BPR (example), 122
BRLT (example), 123
BRS (theorem), 124
BS (theorem), 125
BSCV (subsection, section B), 126
BSM22 (example), 127
BSP4 (example), 128
C (archetype), 129
C (definition), 130
C (notation), 131
C (part), 132
C (Property), 133
C (technique, section PT), 134
CABAK (example), 135
CACN (Property), 136
CAEHW (example), 137
CAF (Property), 138
canonical form
nilpotent linear transformation
example CFNLT, 139
theorem CFNLT, 140
CAV (subsection, section O), 141
Cayley-Hamilton
theorem CHT, 142
CB (section), 143
CB (theorem), 144
CBCV (example), 145
CBM (definition), 146
CBM (subsection, section CB), 147
CBP (example), 148
CC (Property), 149
CCCV (definition), 150
CCCV (notation), 151
CCM (definition), 152
CCM (example), 153
CCM (notation), 154
CCM (theorem), 155
CCN (definition), 156
CCN (notation), 157
CCN (subsection, section CNO), 158
CCRA (theorem), 159
CCRM (theorem), 160
CCT (theorem), 161
CD (subsection, section DM), 162
CD (technique, section PT), 163
CEE (subsection, section EE), 164
CELT (example), 165
CELT (subsection, section CB), 166
CEMS6 (example), 167
CF (section), 168
CFDVS (theorem), 169
CFNLT (example), 170
CFNLT (subsection, section NLT), 171
CFNLT (theorem), 172
CFV (example), 173
change of basis
between polynomials
example CBP, 174
change-of-basis
between column vectors
example CBCV, 175
matrix representation
theorem MRCB, 176
similarity
theorem SCB, 177
theorem CB, 178
change-of-basis matrix
definition CBM, 179
inverse
theorem ICBM, 180
characteristic polynomial
definition CP, 181
degree
theorem DCP, 182
size 3 matrix
example CPMS3, 183
CHT (subsection, section JCF), 184
CHT (theorem), 185
CILT (subsection, section ILT), 186
CILTI (theorem), 187
CIM (subsection, section MISLE), 188
CINM (theorem), 189
CIVLT (example), 190
CIVLT (theorem), 191
CLI (theorem), 192
CLTLT (theorem), 193
CM (definition), 194
CM (Property), 195
CM32 (example), 196
CMCN (Property), 197
CMF (Property), 198
CMI (example), 199
CMIAB (example), 200
CMVEI (theorem), 201
CN (appendix), 202
CNA (definition), 203
CNA (notation), 204
CNA (subsection, section CNO), 205
CNE (definition), 206
CNE (notation), 207
CNM (definition), 208
CNM (notation), 209
CNMB (theorem), 210
CNO (section), 211
CNS1 (example), 212
CNS2 (example), 213
CNSV (example), 214
COB (theorem), 215
coefficient matrix
definition CM, 216
nonsingular
theorem SNCM, 217
column space
as null space
theorem FS, 218
Archetype A
example CSAA, 219
Archetype B
example CSAB, 220
as null space
example CSANS, 221
as null space, Archetype G
example FSAG, 222
as row space
theorem CSRST, 223
basis
theorem BCS, 224
consistent system
theorem CSCS, 225
consistent systems
example CSMCS, 226
isomorphic to range, 227
matrix, 228
nonsingular matrix
theorem CSNM, 229
notation, 230
original columns, Archetype D
example CSOCD, 231
row operations, Archetype I
example CSROI, 232
subspace
theorem CSMS, 233
testing membership
example MCSM, 234
two computations
example CSTW, 235
column vector addition
notation, 236
column vector scalar multiplication
notation, 237
commutativity
column vectors
Property CC, 238
matrices
Property CM, 239
vectors
Property C, 240
complex -space
example VSCV, 241
complex arithmetic
example ACN, 242
complex number
conjugate
example CSCN, 243
modulus
example MSCN, 244
complex number
conjugate
definition CCN, 245
modulus
definition MCN, 246
complex numbers
addition
definition CNA, 247
notation, 248
arithmetic properties
theorem PCNA, 249
equality
definition CNE, 250
notation, 251
multiplication
definition CNM, 252
notation, 253
complex vector space
dimension
theorem DCM, 254
composition
injective linear transformations
theorem CILTI, 255
surjective linear transformations
theorem CSLTS, 256
conjugate
addition
theorem CCRA, 257
column vector
definition CCCV, 258
matrix
definition CCM, 259
notation, 260
multiplication
theorem CCRM, 261
notation, 262
of conjugate of a matrix
theorem CCM, 263
scalar multiplication
theorem CRSM, 264
twice
theorem CCT, 265
vector addition
theorem CRVA, 266
conjugate of a vector
notation, 267
conjugation
matrix addition
theorem CRMA, 268
matrix scalar multiplication
theorem CRMSM, 269
matrix transpose
theorem MCT, 270
consistent linear system, 271
consistent linear systems
theorem CSRN, 272
consistent system
definition CS, 273
constructive proofs
technique C, 274
contradiction
technique CD, 275
contrapositive
technique CP, 276
converse
technique CV, 277
coordinates
orthonormal basis
theorem COB, 278
coordinatization
linear combination of matrices
example CM32, 279
linear independence
theorem CLI, 280
orthonormal basis
example CROB3, 281
example CROB4, 282
spanning sets
theorem CSS, 283
coordinatization principle, 284
coordinatizing
polynomials
example CP2, 285
COV (example), 286
COV (subsection, section LDS), 287
CP (definition), 288
CP (subsection, section VR), 289
CP (technique, section PT), 290
CP2 (example), 291
CPMS3 (example), 292
CPSM (theorem), 293
crazy vector space
example CVSR, 294
properties
example PCVS, 295
CRMA (theorem), 296
CRMSM (theorem), 297
CRN (theorem), 298
CROB3 (example), 299
CROB4 (example), 300
CRS (section), 301
CRS (subsection, section FS), 302
CRSM (theorem), 303
CRVA (theorem), 304
CS (definition), 305
CS (example), 306
CS (subsection, section TSS), 307
CSAA (example), 308
CSAB (example), 309
CSANS (example), 310
CSCN (example), 311
CSCS (theorem), 312
CSIP (example), 313
CSLT (subsection, section SLT), 314
CSLTS (theorem), 315
CSM (definition), 316
CSM (notation), 317
CSMCS (example), 318
CSMS (theorem), 319
CSNM (subsection, section CRS), 320
CSNM (theorem), 321
CSOCD (example), 322
CSRN (theorem), 323
CSROI (example), 324
CSRST (theorem), 325
CSS (theorem), 326
CSSE (subsection, section CRS), 327
CSSOC (subsection, section CRS), 328
CSTW (example), 329
CTD (subsection, section TD), 330
CTLT (example), 331
CUMOS (theorem), 332
curve fitting
polynomial through 5 points
example PTFP, 333
CV (definition), 334
CV (notation), 335
CV (technique, section PT), 336
CVA (definition), 337
CVA (notation), 338
CVC (notation), 339
CVE (definition), 340
CVE (notation), 341
CVS (example), 342
CVS (subsection, section VR), 343
CVSM (definition), 344
CVSM (example), 345
CVSM (notation), 346
CVSR (example), 347
D (acronyms, section PDM), 348
D (archetype), 349
D (chapter), 350
D (definition), 351
D (notation), 352
D (section), 353
D (subsection, section D), 354
D (subsection, section SD), 355
D (technique, section PT), 356
D33M (example), 357
DAB (example), 358
DC (example), 359
DC (technique, section PT), 360
DC (theorem), 361
DCM (theorem), 362
DCN (Property), 363
DCP (theorem), 364
DD (subsection, section DM), 365
DEC (theorem), 366
decomposition
technique DC, 367
DED (theorem), 368
definition
A, 369
AM, 370
AME, 371
B, 372
C, 373
CBM, 374
CCCV, 375
CCM, 376
CCN, 377
CM, 378
CNA, 379
CNE, 380
CNM, 381
CP, 382
CS, 383
CSM, 384
CV, 385
CVA, 386
CVE, 387
CVSM, 388
D, 389
DIM, 390
DM, 391
DS, 392
DZM, 393
EEF, 394
EELT, 395
EEM, 396
ELEM, 397
EM, 398
EO, 399
ES, 400
ESYS, 401
F, 402
GES, 403
GEV, 404
GME, 405
HI, 406
HID, 407
HM, 408
HP, 409
HS, 410
IDLT, 411
IDV, 412
IE, 413
ILT, 414
IM, 415
IMP, 416
IP, 417
IS, 418
IVLT, 419
IVS, 420
JB, 421
JCF, 422
KLT, 423
LC, 424
LCCV, 425
LI, 426
LICV, 427
LNS, 428
LSMR, 429
LSS, 430
LT, 431
LTA, 432
LTC, 433
LTM, 434
LTR, 435
LTSM, 436
M, 437
MA, 438
MCN, 439
ME, 440
MI, 441
MM, 442
MR, 443
MSM, 444
MVP, 445
NLT, 446
NM, 447
NOLT, 448
NOM, 449
NRML, 450
NSM, 451
NV, 452
ONS, 453
OSV, 454
OV, 455
PI, 456
PSM, 457
REM, 458
RLD, 459
RLDCV, 460
RLT, 461
RO, 462
ROLT, 463
ROM, 464
RR, 465
RREF, 466
RSM, 467
S, 468
SC, 469
SE, 470
SET, 471
SI, 472
SIM, 473
SLE, 474
SLT, 475
SM, 476
SOLV, 477
SQM, 478
SRM, 479
SS, 480
SSCV, 481
SSET, 482
SU, 483
SUV, 484
SV, 485
SYM, 486
T, 487
technique D, 488
TM, 489
TS, 490
TSHSE, 491
TSVS, 492
UM, 493
UTM, 494
VM, 495
VOC, 496
VR, 497
VS, 498
VSCV, 499
VSM, 500
ZCV, 501
ZM, 502
DEHD (example), 503
DEM (theorem), 504
DEMMM (theorem), 505
DEMS5 (example), 506
DER (theorem), 507
DERC (theorem), 508
determinant
computed two ways
example TCSD, 509
definition DM, 510
equal rows or columns
theorem DERC, 511
expansion, columns
theorem DEC, 512
expansion, rows
theorem DER, 513
identity matrix
theorem DIM, 514
matrix multiplication
theorem DRMM, 515
nonsingular matrix, 516
notation, 517
row or column multiple
theorem DRCM, 518
row or column swap
theorem DRCS, 519
size 2 matrix
theorem DMST, 520
size 3 matrix
example D33M, 521
transpose
theorem DT, 522
via row operations
example DRO, 523
zero
theorem SMZD, 524
zero row or column
theorem DZRC, 525
zero versus nonzero
example ZNDAB, 526
determinant, upper triangular matrix
example DUTM, 527
determinants
elementary matrices
theorem DEMMM, 528
DF (Property), 529
DF (subsection, section CF), 530
DFS (subsection, section PD), 531
DFS (theorem), 532
DGES (theorem), 533
diagonal matrix
definition DIM, 534
diagonalizable
definition DZM, 535
distinct eigenvalues
example DEHD, 536
theorem DED, 537
full eigenspaces
theorem DMFE, 538
not
example NDMS4, 539
diagonalizable matrix
high power
example HPDM, 540
diagonalization
Archetype B
example DAB, 541
criteria
theorem DC, 542
example DMS3, 543
DIM (definition), 544
DIM (theorem), 545
dimension
crazy vector space
example DC, 546
definition D, 547
notation, 548
polynomial subspace
example DSP4, 549
proper subspaces
theorem PSSD, 550
subspace
example DSM22, 551
direct sum
decomposing zero vector
theorem DSZV, 552
definition DS, 553
dimension
theorem DSD, 554
example SDS, 555
from a basis
theorem DSFB, 556
from one subspace
theorem DSFOS, 557
notation, 558
zero intersection
theorem DSZI, 559
direct sums
linear independence
theorem DSLI, 560
repeated
theorem RDS, 561
distributivity
complex numbers
Property DCN, 562
field
Property DF, 563
distributivity, matrix addition
matrices
Property DMAM, 564
distributivity, scalar addition
column vectors
Property DSAC, 565
matrices
Property DSAM, 566
vectors
Property DSA, 567
distributivity, vector addition
column vectors
Property DVAC, 568
vectors
Property DVA, 569
DLDS (theorem), 570
DM (definition), 571
DM (notation), 572
DM (section), 573
DM (theorem), 574
DMAM (Property), 575
DMFE (theorem), 576
DMHP (subsection, section HP), 577
DMHP (theorem), 578
DMMP (theorem), 579
DMS3 (example), 580
DMST (theorem), 581
DNLT (theorem), 582
DNMMM (subsection, section PDM), 583
DP (theorem), 584
DRCM (theorem), 585
DRCMA (theorem), 586
DRCS (theorem), 587
DRMM (theorem), 588
DRO (example), 589
DRO (subsection, section PDM), 590
DROEM (subsection, section PDM), 591
DS (definition), 592
DS (notation), 593
DS (subsection, section PD), 594
DSA (Property), 595
DSAC (Property), 596
DSAM (Property), 597
DSD (theorem), 598
DSFB (theorem), 599
DSFOS (theorem), 600
DSLI (theorem), 601
DSM22 (example), 602
DSP4 (example), 603
DSZI (theorem), 604
DSZV (theorem), 605
DT (theorem), 606
DUTM (example), 607
DVA (Property), 608
DVAC (Property), 609
DVM (theorem), 610
DVS (subsection, section D), 611
DZM (definition), 612
DZRC (theorem), 613
E (acronyms, section SD), 614
E (archetype), 615
E (chapter), 616
E (technique, section PT), 617
ECEE (subsection, section EE), 618
EDELI (theorem), 619
EDYES (theorem), 620
EE (section), 621
EEE (subsection, section EE), 622
EEF (definition), 623
EEF (subsection, section FS), 624
EELT (definition), 625
EELT (subsection, section CB), 626
EEM (definition), 627
EEM (subsection, section EE), 628
EEMAP (theorem), 629
EENS (example), 630
EER (theorem), 631
EESR (theorem), 632
EHM (subsection, section PEE), 633
eigenspace
as null space
theorem EMNS, 634
definition EM, 635
invariant subspace
theorem EIS, 636
subspace
theorem EMS, 637
eigenvalue
algebraic multiplicity
definition AME, 638
complex
example CEMS6, 639
definition EEM, 640
existence
example CAEHW, 641
theorem EMHE, 642
geometric multiplicity
definition GME, 643
index, 644
linear transformation
definition EELT, 645
multiplicities
example EMMS4, 646
power
theorem EOMP, 647
root of characteristic polynomial
theorem EMRCP, 648
scalar multiple
theorem ESMM, 649
symmetric matrix
example ESMS4, 650
zero
theorem SMZE, 651
eigenvalues
building desired
example BDE, 652
complex, of a linear transformation
example CELT, 653
conjugate pairs
theorem ERMCP, 654
distinct
example DEMS5, 655
example SEE, 656
Hermitian matrices
theorem HMRE, 657
inverse
theorem EIM, 658
maximum number
theorem MNEM, 659
multiplicities
example HMEM5, 660
theorem ME, 661
number
theorem NEM, 662
of a polynomial
theorem EPM, 663
size 3 matrix
example EMS3, 664
example ESMS3, 665
transpose
theorem ETM, 666
eigenvalues, eigenvectors
vector, matrix representations
theorem EER, 667
eigenvector, 668
linear transformation, 669
eigenvectors, 670
conjugate pairs, 671
Hermitian matrices
theorem HMOE, 672
linear transformation
example ELTBM, 673
example ELTBP, 674
linearly independent
theorem EDELI, 675
of a linear transformation
example ELTT, 676
EILT (subsection, section ILT), 677
EIM (theorem), 678
EIS (example), 679
EIS (theorem), 680
ELEM (definition), 681
ELEM (notation), 682
elementary matrices
definition ELEM, 683
determinants
theorem DEM, 684
nonsingular
theorem EMN, 685
notation, 686
row operations
example EMRO, 687
theorem EMDRO, 688
ELIS (theorem), 689
ELTBM (example), 690
ELTBP (example), 691
ELTT (example), 692
EM (definition), 693
EM (subsection, section DM), 694
EMDRO (theorem), 695
EMHE (theorem), 696
EMMS4 (example), 697
EMMVP (theorem), 698
EMN (theorem), 699
EMNS (theorem), 700
EMP (theorem), 701
empty set, 702
notation, 703
EMRCP (theorem), 704
EMRO (example), 705
EMS (theorem), 706
EMS3 (example), 707
ENLT (theorem), 708
EO (definition), 709
EOMP (theorem), 710
EOPSS (theorem), 711
EPM (theorem), 712
EPSM (theorem), 713
equal matrices
via equal matrix-vector products
theorem EMMVP, 714
equation operations
definition EO, 715
theorem EOPSS, 716
equivalence statements
technique E, 717
equivalences
technique ME, 718
equivalent systems
definition ESYS, 719
ERMCP (theorem), 720
ES (definition), 721
ES (notation), 722
ESEO (subsection, section SSLE), 723
ESLT (subsection, section SLT), 724
ESMM (theorem), 725
ESMS3 (example), 726
ESMS4 (example), 727
ESYS (definition), 728
ETM (theorem), 729
EVS (subsection, section VS), 730
example
AALC, 731
ABLC, 732
ABS, 733
ACN, 734
AHSAC, 735
AIVLT, 736
ALT, 737
ALTMM, 738
AM, 739
AMAA, 740
ANILT, 741
ANM, 742
AOS, 743
ASC, 744
AVR, 745
BC, 746
BDE, 747
BDM22, 748
BM, 749
BP, 750
BPR, 751
BRLT, 752
BSM22, 753
BSP4, 754
CABAK, 755
CAEHW, 756
CBCV, 757
CBP, 758
CCM, 759
CELT, 760
CEMS6, 761
CFNLT, 762
CFV, 763
CIVLT, 764
CM32, 765
CMI, 766
CMIAB, 767
CNS1, 768
CNS2, 769
CNSV, 770
COV, 771
CP2, 772
CPMS3, 773
CROB3, 774
CROB4, 775
CS, 776
CSAA, 777
CSAB, 778
CSANS, 779
CSCN, 780
CSIP, 781
CSMCS, 782
CSOCD, 783
CSROI, 784
CSTW, 785
CTLT, 786
CVS, 787
CVSM, 788
CVSR, 789
D33M, 790
DAB, 791
DC, 792
DEHD, 793
DEMS5, 794
DMS3, 795
DRO, 796
DSM22, 797
DSP4, 798
DUTM, 799
EENS, 800
EIS, 801
ELTBM, 802
ELTBP, 803
ELTT, 804
EMMS4, 805
EMRO, 806
EMS3, 807
ESMS3, 808
ESMS4, 809
FDV, 810
FF8, 811
FRAN, 812
FS1, 813
FS2, 814
FSAG, 815
GE4, 816
GE6, 817
GENR6, 818
GSTV, 819
HISAA, 820
HISAD, 821
HMEM5, 822
HP, 823
HPDM, 824
HUSAB, 825
IAP, 826
IAR, 827
IAS, 828
IAV, 829
ILTVR, 830
IM, 831
IM11, 832
IS, 833
ISJB, 834
ISMR4, 835
ISMR6, 836
ISSI, 837
IVSAV, 838
JB4, 839
JCF10, 840
KPNLT, 841
KVMR, 842
LCM, 843
LDCAA, 844
LDHS, 845
LDP4, 846
LDRN, 847
LDS, 848
LIC, 849
LICAB, 850
LIHS, 851
LIM32, 852
LINSB, 853
LIP4, 854
LIS, 855
LLDS, 856
LNS, 857
LTDB1, 858
LTDB2, 859
LTDB3, 860
LTM, 861
LTPM, 862
LTPP, 863
LTRGE, 864
MA, 865
MBC, 866
MCSM, 867
MFLT, 868
MI, 869
MIVS, 870
MMNC, 871
MNSLE, 872
MOLT, 873
MPMR, 874
MRBE, 875
MRCM, 876
MSCN, 877
MSM, 878
MTV, 879
MWIAA, 880
NDMS4, 881
NIAO, 882
NIAQ, 883
NIAQR, 884
NIDAU, 885
NJB5, 886
NKAO, 887
NLT, 888
NM, 889
NM62, 890
NM64, 891
NM83, 892
NRREF, 893
NSAO, 894
NSAQ, 895
NSAQR, 896
NSC2A, 897
NSC2S, 898
NSC2Z, 899
NSDAT, 900
NSDS, 901
NSE, 902
NSEAI, 903
NSLE, 904
NSLIL, 905
NSNM, 906
NSR, 907
NSS, 908
OLTTR, 909
ONFV, 910
ONTV, 911
OSGMD, 912
OSMC, 913
PCVS, 914
PM, 915
PSHS, 916
PTFP, 917
PTM, 918
PTMEE, 919
RAO, 920
RES, 921
RNM, 922
RNSM, 923
ROD2, 924
ROD4, 925
RREF, 926
RREFN, 927
RRTI, 928
RS, 929
RSAI, 930
RSB, 931
RSC5, 932
RSNS, 933
RSREM, 934
RSSC4, 935
RVMR, 936
S, 937
SAA, 938
SAB, 939
SABMI, 940
SAE, 941
SAN, 942
SAR, 943
SAV, 944
SC, 945
SC3, 946
SCAA, 947
SCAB, 948
SCAD, 949
SDS, 950
SEE, 951
SEEF, 952
SETM, 953
SI, 954
SM2Z7, 955
SM32, 956
SMLT, 957
SMS3, 958
SMS5, 959
SP4, 960
SPIAS, 961
SRR, 962
SS, 963
SS6W, 964
SSC, 965
SSET, 966
SSM22, 967
SSNS, 968
SSP, 969
SSP4, 970
STLT, 971
STNE, 972
SU, 973
SUVOS, 974
SVP4, 975
SYM, 976
TCSD, 977
TD4, 978
TDEE6, 979
TDSSE, 980
TIS, 981
TIVS, 982
TKAP, 983
TLC, 984
TM, 985
TMP, 986
TOV, 987
TREM, 988
TTS, 989
UM3, 990
UPM, 991
US, 992
USR, 993
VA, 994
VESE, 995
VFS, 996
VFSAD, 997
VFSAI, 998
VFSAL, 999
VM4, 1000
VRC4, 1001
VRP2, 1002
VSCV, 1003
VSF, 1004
VSIM5, 1005
VSIS, 1006
VSM, 1007
VSP, 1008
VSPUD, 1009
VSS, 1010
ZNDAB, 1011
EXC (subsection, section B), 1012
EXC (subsection, section CB), 1013
EXC (subsection, section CF), 1014
EXC (subsection, section CRS), 1015
EXC (subsection, section D), 1016
EXC (subsection, section DM), 1017
EXC (subsection, section EE), 1018
EXC (subsection, section F), 1019
EXC (subsection, section FS), 1020
EXC (subsection, section HP), 1021
EXC (subsection, section HSE), 1022
EXC (subsection, section ILT), 1023
EXC (subsection, section IVLT), 1024
EXC (subsection, section LC), 1025
EXC (subsection, section LDS), 1026
EXC (subsection, section LI), 1027
EXC (subsection, section LISS), 1028
EXC (subsection, section LT), 1029
EXC (subsection, section MINM), 1030
EXC (subsection, section MISLE), 1031
EXC (subsection, section MM), 1032
EXC (subsection, section MO), 1033
EXC (subsection, section MR), 1034
EXC (subsection, section NM), 1035
EXC (subsection, section O), 1036
EXC (subsection, section PD), 1037
EXC (subsection, section PDM), 1038
EXC (subsection, section PEE), 1039
EXC (subsection, section PSM), 1040
EXC (subsection, section RREF), 1041
EXC (subsection, section S), 1042
EXC (subsection, section SD), 1043
EXC (subsection, section SLT), 1044
EXC (subsection, section SS), 1045
EXC (subsection, section SSLE), 1046
EXC (subsection, section T), 1047
EXC (subsection, section TSS), 1048
EXC (subsection, section VO), 1049
EXC (subsection, section VR), 1050
EXC (subsection, section VS), 1051
EXC (subsection, section WILA), 1052
extended echelon form
submatrices
example SEEF, 1053
extended reduced row-echelon form
properties
theorem PEEF, 1054
F (archetype), 1055
F (definition), 1056
F (section), 1057
F (subsection, section F), 1058
FDV (example), 1059
FF (subsection, section F), 1060
FF8 (example), 1061
field
definition F, 1062
FIMP (theorem), 1063
finite field
size 8
example FF8, 1064
four subsets
example FS1, 1065
example FS2, 1066
four subspaces
dimension
theorem DFS, 1067
FRAN (example), 1068
free variables
example CFV, 1069
free variables, number
theorem FVCS, 1070
free, independent variables
example FDV, 1071
FS (section), 1072
FS (subsection, section FS), 1073
FS (theorem), 1074
FS1 (example), 1075
FS2 (example), 1076
FSAG (example), 1077
FTMR (theorem), 1078
FV (subsection, section TSS), 1079
FVCS (theorem), 1080
G (archetype), 1081
G (theorem), 1082
GE4 (example), 1083
GE6 (example), 1084
GEE (subsection, section IS), 1085
GEK (theorem), 1086
generalized eigenspace
as kernel
theorem GEK, 1087
definition GES, 1088
dimension
theorem DGES, 1089
dimension 4 domain
example GE4, 1090
dimension 6 domain
example GE6, 1091
invariant subspace
theorem GESIS, 1092
nilpotent restriction
theorem RGEN, 1093
nilpotent restrictions, dimension 6 domain
example GENR6, 1094
notation, 1095
generalized eigenspace decomposition
theorem GESD, 1096
generalized eigenvector
definition GEV, 1097
GENR6 (example), 1098
GES (definition), 1099
GES (notation), 1100
GESD (subsection, section JCF), 1101
GESD (theorem), 1102
GESIS (theorem), 1103
GEV (definition), 1104
GFDL (appendix), 1105
GME (definition), 1106
goldilocks
theorem G, 1107
Gram-Schmidt
column vectors
theorem GSP, 1108
three vectors
example GSTV, 1109
gram-schmidt
mathematica, 1110
GS (technique, section PT), 1111
GSP (subsection, section O), 1112
GSP (theorem), 1113
GSP.MMA (computation, section MMA), 1114
GSTV (example), 1115
GT (subsection, section PD), 1116
H (archetype), 1117
Hadamard Identity
notation, 1118
Hadamard identity
definition HID, 1119
Hadamard Inverse
notation, 1120
Hadamard inverse
definition HI, 1121
Hadamard Product
Diagonalizable Matrices
theorem DMHP, 1122
notation, 1123
Hadamard product
commutativity
theorem HPC, 1124
definition HP, 1125
diagonal matrices
theorem DMMP, 1126
distributivity
theorem HPDAA, 1127
example HP, 1128
identity
theorem HPHID, 1129
inverse
theorem HPHI, 1130
scalar matrix multiplication
theorem HPSMM, 1131
hermitian
definition HM, 1132
Hermitian matrix
inner product
theorem HMIP, 1133
HI (definition), 1134
HI (notation), 1135
HID (definition), 1136
HID (notation), 1137
HISAA (example), 1138
HISAD (example), 1139
HM (definition), 1140
HM (subsection, section MM), 1141
HMEM5 (example), 1142
HMIP (theorem), 1143
HMOE (theorem), 1144
HMRE (theorem), 1145
HMVEI (theorem), 1146
homogeneous system
consistent
theorem HSC, 1147
definition HS, 1148
infinitely many solutions
theorem HMVEI, 1149
homogeneous systems
linear independence, 1150
homogenous system
Archetype C
example AHSAC, 1151
HP (definition), 1152
HP (example), 1153
HP (notation), 1154
HP (section), 1155
HPC (theorem), 1156
HPDAA (theorem), 1157
HPDM (example), 1158
HPHI (theorem), 1159
HPHID (theorem), 1160
HPSMM (theorem), 1161
HS (definition), 1162
HSC (theorem), 1163
HSE (section), 1164
HUSAB (example), 1165
I (archetype), 1166
I (technique, section PT), 1167
IAP (example), 1168
IAR (example), 1169
IAS (example), 1170
IAV (example), 1171
ICBM (theorem), 1172
ICLT (theorem), 1173
identities
technique PI, 1174
identity matrix
determinant, 1175
example IM, 1176
notation, 1177
IDLT (definition), 1178
IDV (definition), 1179
IE (definition), 1180
IE (notation), 1181
IFDVS (theorem), 1182
IILT (theorem), 1183
ILT (definition), 1184
ILT (section), 1185
ILTB (theorem), 1186
ILTD (subsection, section ILT), 1187
ILTD (theorem), 1188
ILTIS (theorem), 1189
ILTLI (subsection, section ILT), 1190
ILTLI (theorem), 1191
ILTLT (theorem), 1192
ILTVR (example), 1193
IM (definition), 1194
IM (example), 1195
IM (notation), 1196
IM (subsection, section MISLE), 1197
IM11 (example), 1198
IMILT (theorem), 1199
IMP (definition), 1200
IMR (theorem), 1201
inconsistent linear systems
theorem ISRN, 1202
independent, dependent variables
definition IDV, 1203
indesxstring
example SM2Z7, 1204
example SSET, 1205
index
eigenvalue
definition IE, 1206
notation, 1207
indexstring
theorem DRCMA, 1208
theorem OBUTR, 1209
theorem UMCOB, 1210
induction
technique I, 1211
infinite solution set
example ISSI, 1212
infinite solutions,
example IS, 1213
injective
example IAP, 1214
example IAR, 1215
not
example NIAO, 1216
example NIAQ, 1217
example NIAQR, 1218
not, by dimension
example NIDAU, 1219
polynomials to matrices
example IAV, 1220
injective linear transformation
bases
theorem ILTB, 1221
injective linear transformations
dimension
theorem ILTD, 1222
inner product
anti-commutative
theorem IPAC, 1223
example CSIP, 1224
norm
theorem IPN, 1225
notation, 1226
positive
theorem PIP, 1227
scalar multiplication
theorem IPSM, 1228
vector addition
theorem IPVA, 1229
integers
mod
definition IMP, 1230
mod , field
theorem FIMP, 1231
mod 11
example IM11, 1232
interpolating polynomial
theorem IP, 1233
invariant subspace
definition IS, 1234
eigenspace, 1235
eigenspaces
example EIS, 1236
example TIS, 1237
Jordan block
example ISJB, 1238
kernels of powers
theorem KPIS, 1239
inverse
composition of linear transformations
theorem ICLT, 1240
example CMI, 1241
example MI, 1242
notation, 1243
of a matrix, 1244
invertible linear transformation
defined by invertible matrix
theorem IMILT, 1245
invertible linear transformations
composition
theorem CIVLT, 1246
computing
example CIVLT, 1247
IP (definition), 1248
IP (notation), 1249
IP (subsection, section O), 1250
IP (theorem), 1251
IPAC (theorem), 1252
IPN (theorem), 1253
IPSM (theorem), 1254
IPVA (theorem), 1255
IS (definition), 1256
IS (example), 1257
IS (section), 1258
IS (subsection, section IS), 1259
ISJB (example), 1260
ISMR4 (example), 1261
ISMR6 (example), 1262
isomorphic
multiple vector spaces
example MIVS, 1263
vector spaces
example IVSAV, 1264
isomorphic vector spaces
dimension
theorem IVSED, 1265
example TIVS, 1266
ISRN (theorem), 1267
ISSI (example), 1268
ITMT (theorem), 1269
IV (subsection, section IVLT), 1270
IVLT (definition), 1271
IVLT (section), 1272
IVLT (subsection, section IVLT), 1273
IVLT (subsection, section MR), 1274
IVS (definition), 1275
IVSAV (example), 1276
IVSED (theorem), 1277
J (archetype), 1278
JB (definition), 1279
JB (notation), 1280
JB4 (example), 1281
JCF (definition), 1282
JCF (section), 1283
JCF (subsection, section JCF), 1284
JCF10 (example), 1285
JCFLT (theorem), 1286
Jordan block
definition JB, 1287
nilpotent
theorem NJB, 1288
notation, 1289
size 4
example JB4, 1290
Jordan canonical form
definition JCF, 1291
size 10
example JCF10, 1292
K (archetype), 1293
kernel
injective linear transformation
theorem KILT, 1294
isomorphic to null space
theorem KNSI, 1295
linear transformation
example NKAO, 1296
notation, 1297
of a linear transformation
definition KLT, 1298
pre-image, 1299
subspace
theorem KLTS, 1300
trivial
example TKAP, 1301
via matrix representation
example KVMR, 1302
KILT (theorem), 1303
KLT (definition), 1304
KLT (notation), 1305
KLT (subsection, section ILT), 1306
KLTS (theorem), 1307
KNSI (theorem), 1308
KPI (theorem), 1309
KPIS (theorem), 1310
KPLT (theorem), 1311
KPNLT (example), 1312
KPNLT (theorem), 1313
KVMR (example), 1314
L (archetype), 1315
L (technique, section PT), 1316
LA (subsection, section WILA), 1317
LC (definition), 1318
LC (section), 1319
LC (subsection, section LC), 1320
LC (technique, section PT), 1321
LCCV (definition), 1322
LCM (example), 1323
LDCAA (example), 1324
LDHS (example), 1325
LDP4 (example), 1326
LDRN (example), 1327
LDS (example), 1328
LDS (section), 1329
LDSS (subsection, section LDS), 1330
least squares
minimizes residuals
theorem LSMR, 1331
least squares solution
definition LSS, 1332
left null space
as row space, 1333
definition LNS, 1334
example LNS, 1335
notation, 1336
subspace
theorem LNSMS, 1337
lemma
technique LC, 1338
LI (definition), 1339
LI (section), 1340
LI (subsection, section LISS), 1341
LIC (example), 1342
LICAB (example), 1343
LICV (definition), 1344
LIHS (example), 1345
LIM32 (example), 1346
linear combination
system of equations
example ABLC, 1347
definition LC, 1348
definition LCCV, 1349
example TLC, 1350
linear transformation, 1351
matrices
example LCM, 1352
system of equations
example AALC, 1353
linear combinations
solutions to linear systems
theorem SLSLC, 1354
linear dependence
more vectors than size
theorem MVSLD, 1355
linear independence
definition LI, 1356
definition LICV, 1357
homogeneous systems
theorem LIVHS, 1358
injective linear transformation
theorem ILTLI, 1359
matrices
example LIM32, 1360
orthogonal, 1361
r and n
theorem LIVRN, 1362
linear solve
mathematica, 1363
linear system
consistent
theorem RCLS, 1364
matrix representation
definition LSMR, 1365
notation, 1366
linear systems
notation
example MNSLE, 1367
example NSLE, 1368
linear transformation
polynomials to polynomials
example LTPP, 1369
addition
definition LTA, 1370
theorem MLTLT, 1371
theorem SLTLT, 1372
as matrix multiplication
example ALTMM, 1373
basis of range
example BRLT, 1374
checking
example ALT, 1375
composition
definition LTC, 1376
theorem CLTLT, 1377
defined by a matrix
example LTM, 1378
defined on a basis
example LTDB1, 1379
example LTDB2, 1380
example LTDB3, 1381
theorem LTDB, 1382
definition LT, 1383
identity
definition IDLT, 1384
injection
definition ILT, 1385
inverse
theorem ILTLT, 1386
inverse of inverse
theorem IILT, 1387
invertible
definition IVLT, 1388
example AIVLT, 1389
invertible, injective and surjective
theorem ILTIS, 1390
Jordan canonical form
theorem JCFLT, 1391
kernels of powers
theorem KPLT, 1392
linear combination
theorem LTLC, 1393
matrix of, 1394
example MFLT, 1395
example MOLT, 1396
not
example NLT, 1397
not invertible
example ANILT, 1398
notation, 1399
polynomials to matrices
example LTPM, 1400
rank plus nullity
theorem RPNDD, 1401
restriction
definition LTR, 1402
notation, 1403
scalar multiple
example SMLT, 1404
scalar multiplication
definition LTSM, 1405
spanning range
theorem SSRLT, 1406
sum
example STLT, 1407
surjection
definition SLT, 1408
vector space of, 1409
zero vector
theorem LTTZZ, 1410
linear transformation inverse
via matrix representation
example ILTVR, 1411
linear transformation restriction
on generalized eigenspace
example LTRGE, 1412
linear transformations
compositions
example CTLT, 1413
from matrices
theorem MBLT, 1414
linearly dependent
example LDRN, 1415
via homogeneous system
example LDHS, 1416
linearly dependent columns
Archetype A
example LDCAA, 1417
linearly dependent set
example LDS, 1418
linear combinations within
theorem DLDS, 1419
polynomials
example LDP4, 1420
linearly independent
crazy vector space
example LIC, 1421
extending sets
theorem ELIS, 1422
polynomials
example LIP4, 1423
via homogeneous system
example LIHS, 1424
linearly independent columns
Archetype B
example LICAB, 1425
linearly independent set
example LIS, 1426
example LLDS, 1427
LINM (subsection, section LI), 1428
LINSB (example), 1429
LIP4 (example), 1430
LIS (example), 1431
LISS (section), 1432
LISV (subsection, section LI), 1433
LIVHS (theorem), 1434
LIVRN (theorem), 1435
LLDS (example), 1436
LNS (definition), 1437
LNS (example), 1438
LNS (notation), 1439
LNS (subsection, section FS), 1440
LNSMS (theorem), 1441
lower triangular matrix
definition LTM, 1442
LS.MMA (computation, section MMA), 1443
LSMR (definition), 1444
LSMR (notation), 1445
LSMR (theorem), 1446
LSS (definition), 1447
LT (acronyms, section IVLT), 1448
LT (chapter), 1449
LT (definition), 1450
LT (notation), 1451
LT (section), 1452
LT (subsection, section LT), 1453
LTA (definition), 1454
LTC (definition), 1455
LTDB (theorem), 1456
LTDB1 (example), 1457
LTDB2 (example), 1458
LTDB3 (example), 1459
LTLC (subsection, section LT), 1460
LTLC (theorem), 1461
LTM (definition), 1462
LTM (example), 1463
LTPM (example), 1464
LTPP (example), 1465
LTR (definition), 1466
LTR (notation), 1467
LTRGE (example), 1468
LTSM (definition), 1469
LTTZZ (theorem), 1470
M (acronyms, section FS), 1471
M (archetype), 1472
M (chapter), 1473
M (definition), 1474
M (notation), 1475
MA (definition), 1476
MA (example), 1477
MA (notation), 1478
MACN (Property), 1479
MAF (Property), 1480
MAP (subsection, section SVD), 1481
mathematica
gram-schmidt (computation), 1482
linear solve (computation), 1483
matrix entry (computation), 1484
matrix inverse (computation), 1485
matrix multiplication (computation), 1486
null space (computation), 1487
row reduce (computation), 1488
transpose of a matrix (computation), 1489
vector form of solutions (computation), 1490
vector linear combinations (computation), 1491
mathematical language
technique L, 1492
matrix
addition
definition MA, 1493
notation, 1494
augmented
definition AM, 1495
column space
definition CSM, 1496
complex conjugate
example CCM, 1497
definition M, 1498
equality
definition ME, 1499
notation, 1500
example AM, 1501
identity
definition IM, 1502
inverse
definition MI, 1503
nonsingular
definition NM, 1504
notation, 1505
of a linear transformation
theorem MLTCV, 1506
product
example PTM, 1507
example PTMEE, 1508
product with vector
definition MVP, 1509
rectangular, 1510
row space
definition RSM, 1511
scalar multiplication
definition MSM, 1512
notation, 1513
singular, 1514
square
definition SQM, 1515
submatrices
example SS, 1516
submatrix
definition SM, 1517
symmetric
definition SYM, 1518
transpose
definition TM, 1519
unitary
definition UM, 1520
unitary is invertible
theorem UMI, 1521
zero
definition ZM, 1522
matrix addition
example MA, 1523
matrix components
notation, 1524
matrix entry
mathematica, 1525
ti83, 1526
ti86, 1527
matrix inverse
Archetype B, 1528
computation
theorem CINM, 1529
mathematica, 1530
nonsingular matrix
theorem NI, 1531
of a matrix inverse
theorem MIMI, 1532
one-sided
theorem OSIS, 1533
product
theorem SS, 1534
scalar multiple
theorem MISM, 1535
size 2 matrices
theorem TTMI, 1536
transpose
theorem MIT, 1537
uniqueness
theorem MIU, 1538
matrix multiplication
adjoints
theorem MMAD, 1539
associativity
theorem MMA, 1540
complex conjugation
theorem MMCC, 1541
definition MM, 1542
distributivity
theorem MMDAA, 1543
entry-by-entry
theorem EMP, 1544
identity matrix
theorem MMIM, 1545
inner product
theorem MMIP, 1546
mathematica, 1547
noncommutative
example MMNC, 1548
scalar matrix multiplication
theorem MMSMM, 1549
systems of linear equations
theorem SLEMM, 1550
transposes
theorem MMT, 1551
zero matrix
theorem MMZM, 1552
matrix product
as composition of linear transformations
example MPMR, 1553
matrix representation
basis of eigenvectors
example MRBE, 1554
composition of linear transformations
theorem MRCLT, 1555
definition MR, 1556
invertible
theorem IMR, 1557
multiple of a linear transformation
theorem MRMLT, 1558
restriction to generalized eigenspace
theorem MRRGE, 1559
sum of linear transformations
theorem MRSLT, 1560
theorem FTMR, 1561
upper triangular
theorem UTMR, 1562
matrix representations
converting with change-of-basis
example MRCM, 1563
example OLTTR, 1564
matrix scalar multiplication
example MSM, 1565
matrix vector space
dimension
theorem DM, 1566
matrix-adjoint product
eigenvalues, eigenvectors
theorem EEMAP, 1567
matrix-vector product
example MTV, 1568
notation, 1569
MBC (example), 1570
MBLT (theorem), 1571
MC (notation), 1572
MCC (subsection, section MO), 1573
MCCN (Property), 1574
MCF (Property), 1575
MCN (definition), 1576
MCN (subsection, section CNO), 1577
MCSM (example), 1578
MCT (theorem), 1579
MD (chapter), 1580
ME (definition), 1581
ME (notation), 1582
ME (subsection, section PEE), 1583
ME (technique, section PT), 1584
ME (theorem), 1585
ME.MMA (computation, section MMA), 1586
ME.TI83 (computation, section TI83), 1587
ME.TI86 (computation, section TI86), 1588
MEASM (subsection, section MO), 1589
MFLT (example), 1590
MI (definition), 1591
MI (example), 1592
MI (notation), 1593
MI.MMA (computation, section MMA), 1594
MICN (Property), 1595
MIF (Property), 1596
MIMI (theorem), 1597
MINM (section), 1598
MISLE (section), 1599
MISM (theorem), 1600
MIT (theorem), 1601
MIU (theorem), 1602
MIVS (example), 1603
MLT (subsection, section LT), 1604
MLTCV (theorem), 1605
MLTLT (theorem), 1606
MM (definition), 1607
MM (section), 1608
MM (subsection, section MM), 1609
MM.MMA (computation, section MMA), 1610
MMA (section), 1611
MMA (theorem), 1612
MMAD (theorem), 1613
MMCC (theorem), 1614
MMDAA (theorem), 1615
MMEE (subsection, section MM), 1616
MMIM (theorem), 1617
MMIP (theorem), 1618
MMNC (example), 1619
MMSMM (theorem), 1620
MMT (theorem), 1621
MMZM (theorem), 1622
MNEM (theorem), 1623
MNSLE (example), 1624
MO (section), 1625
MOLT (example), 1626
more variables than equations
example OSGMD, 1627
theorem CMVEI, 1628
MPMR (example), 1629
MR (definition), 1630
MR (section), 1631
MRBE (example), 1632
MRCB (theorem), 1633
MRCLT (theorem), 1634
MRCM (example), 1635
MRMLT (theorem), 1636
MRRGE (theorem), 1637
MRS (subsection, section CB), 1638
MRSLT (theorem), 1639
MSCN (example), 1640
MSM (definition), 1641
MSM (example), 1642
MSM (notation), 1643
MTV (example), 1644
multiplicative associativity
complex numbers
Property MACN, 1645
multiplicative closure
complex numbers
Property MCCN, 1646
field
Property MCF, 1647
multiplicative commuativity
complex numbers
Property CMCN, 1648
multiplicative inverse
complex numbers
Property MICN, 1649
MVNSE (subsection, section RREF), 1650
MVP (definition), 1651
MVP (notation), 1652
MVP (subsection, section MM), 1653
MVSLD (theorem), 1654
MWIAA (example), 1655
N (archetype), 1656
N (subsection, section O), 1657
N (technique, section PT), 1658
NDMS4 (example), 1659
negation of statements
technique N, 1660
NEM (theorem), 1661
NI (theorem), 1662
NIAO (example), 1663
NIAQ (example), 1664
NIAQR (example), 1665
NIDAU (example), 1666
nilpotent
linear transformation
definition NLT, 1667
NJB (theorem), 1668
NJB5 (example), 1669
NKAO (example), 1670
NLT (definition), 1671
NLT (example), 1672
NLT (section), 1673
NLT (subsection, section NLT), 1674
NLTFO (subsection, section LT), 1675
NM (definition), 1676
NM (example), 1677
NM (section), 1678
NM (subsection, section NM), 1679
NM (subsection, section OD), 1680
NM62 (example), 1681
NM64 (example), 1682
NM83 (example), 1683
NME1 (theorem), 1684
NME2 (theorem), 1685
NME3 (theorem), 1686
NME4 (theorem), 1687
NME5 (theorem), 1688
NME6 (theorem), 1689
NME7 (theorem), 1690
NME8 (theorem), 1691
NME9 (theorem), 1692
NMI (subsection, section MINM), 1693
NMLIC (theorem), 1694
NMPEM (theorem), 1695
NMRRI (theorem), 1696
NMTNS (theorem), 1697
NMUS (theorem), 1698
NOILT (theorem), 1699
NOLT (definition), 1700
NOLT (notation), 1701
NOM (definition), 1702
NOM (notation), 1703
nonsingular
columns as basis
theorem CNMB, 1704
nonsingular matrices
linearly independent columns
theorem NMLIC, 1705
nonsingular matrix
Archetype B
example NM, 1706
column space, 1707
elemntary matrices
theorem NMPEM, 1708
equivalences
theorem NME1, 1709
theorem NME2, 1710
theorem NME3, 1711
theorem NME4, 1712
theorem NME5, 1713
theorem NME6, 1714
theorem NME7, 1715
theorem NME8, 1716
theorem NME9, 1717
matrix inverse, 1718
null space
example NSNM, 1719
nullity, 1720
product of nonsingular matrices
theorem NPNT, 1721
rank
theorem RNNM, 1722
row-reduced
theorem NMRRI, 1723
trivial null space
theorem NMTNS, 1724
unique solutions
theorem NMUS, 1725
nonsingular matrix, row-reduced
example NSR, 1726
norm
example CNSV, 1727
inner product, 1728
notation, 1729
normal matrix
definition NRML, 1730
example ANM, 1731
orthonormal basis, 1732
notation
A, 1733
AM, 1734
C, 1735
CCCV, 1736
CCM, 1737
CCN, 1738
CNA, 1739
CNE, 1740
CNM, 1741
CSM, 1742
CV, 1743
CVA, 1744
CVC, 1745
CVE, 1746
CVSM, 1747
D, 1748
DM, 1749
DS, 1750
ELEM, 1751
ES, 1752
GES, 1753
HI, 1754
HID, 1755
HP, 1756
IE, 1757
IM, 1758
IP, 1759
JB, 1760
KLT, 1761
LNS, 1762
LSMR, 1763
LT, 1764
LTR, 1765
M, 1766
MA, 1767
MC, 1768
ME, 1769
MI, 1770
MSM, 1771
MVP, 1772
NOLT, 1773
NOM, 1774
NSM, 1775
NV, 1776
RLT, 1777
RO, 1778
ROLT, 1779
ROM, 1780
RREFA, 1781
RSM, 1782
SC, 1783
SE, 1784
SETM, 1785
SI, 1786
SM, 1787
SRM, 1788
SSET, 1789
SSV, 1790
SU, 1791
SUV, 1792
T, 1793
TM, 1794
VSCV, 1795
VSM, 1796
ZCV, 1797
ZM, 1798
notation for a linear system
example NSE, 1799
NPNT (theorem), 1800
NRFO (subsection, section MR), 1801
NRML (definition), 1802
NRREF (example), 1803
NS.MMA (computation, section MMA), 1804
NSAO (example), 1805
NSAQ (example), 1806
NSAQR (example), 1807
NSC2A (example), 1808
NSC2S (example), 1809
NSC2Z (example), 1810
NSDAT (example), 1811
NSDS (example), 1812
NSE (example), 1813
NSEAI (example), 1814
NSLE (example), 1815
NSLIL (example), 1816
NSM (definition), 1817
NSM (notation), 1818
NSM (subsection, section HSE), 1819
NSMS (theorem), 1820
NSNM (example), 1821
NSNM (subsection, section NM), 1822
NSR (example), 1823
NSS (example), 1824
NSSLI (subsection, section LI), 1825
Null space
as a span
example NSDS, 1826
null space
Archetype I
example NSEAI, 1827
basis
theorem BNS, 1828
computation
example CNS1, 1829
example CNS2, 1830
isomorphic to kernel, 1831
linearly independent basis
example LINSB, 1832
mathematica, 1833
matrix
definition NSM, 1834
nonsingular matrix, 1835
notation, 1836
singular matrix, 1837
spanning set
example SSNS, 1838
theorem SSNS, 1839
subspace
theorem NSMS, 1840
null space span, linearly independent
Archetype L
example NSLIL, 1841
nullity
computing, 1842
injective linear transformation
theorem NOILT, 1843
linear transformation
definition NOLT, 1844
matrix, 1845
definition NOM, 1846
notation, 1847, 1848
square matrix, 1849
NV (definition), 1850
NV (notation), 1851
NVM (theorem), 1852
O (archetype), 1853
O (Property), 1854
O (section), 1855
OBC (subsection, section B), 1856
OBNM (theorem), 1857
OBUTR (theorem), 1858
OC (Property), 1859
OCN (Property), 1860
OD (section), 1861
OD (subsection, section OD), 1862
OD (theorem), 1863
OF (Property), 1864
OLTTR (example), 1865
OM (Property), 1866
one
column vectors
Property OC, 1867
complex numbers
Property OCN, 1868
field
Property OF, 1869
matrices
Property OM, 1870
vectors
Property O, 1871
ONFV (example), 1872
ONS (definition), 1873
ONTV (example), 1874
orthogonal
linear independence
theorem OSLI, 1875
set
example AOS, 1876
set of vectors
definition OSV, 1877
vector pairs
definition OV, 1878
orthogonal vectors
example TOV, 1879
orthonormal
definition ONS, 1880
matrix columns
example OSMC, 1881
orthonormal basis
normal matrix
theorem OBNM, 1882
orthonormal diagonalization
theorem OD, 1883
orthonormal set
four vectors
example ONFV, 1884
three vectors
example ONTV, 1885
OSGMD (example), 1886
OSIS (theorem), 1887
OSLI (theorem), 1888
OSMC (example), 1889
OSV (definition), 1890
OV (definition), 1891
OV (subsection, section O), 1892
P (appendix), 1893
P (archetype), 1894
P (technique, section PT), 1895
particular solutions
example PSHS, 1896
PCNA (theorem), 1897
PCVS (example), 1898
PD (section), 1899
PDM (section), 1900
PDM (theorem), 1901
PEE (section), 1902
PEEF (theorem), 1903
PI (definition), 1904
PI (subsection, section LT), 1905
PI (technique, section PT), 1906
PIP (theorem), 1907
PM (example), 1908
PM (subsection, section EE), 1909
PMI (subsection, section MISLE), 1910
PMM (subsection, section MM), 1911
PMR (subsection, section MR), 1912
PNLT (subsection, section NLT), 1913
POD (section), 1914
polar decomposition
theorem PDM, 1915
polynomial
of a matrix
example PM, 1916
polynomial vector space
dimension
theorem DP, 1917
positive semi-definite
creating
theorem CPSM, 1918
positive semi-definite matrix
definition PSM, 1919
eigenvalues
theorem EPSM, 1920
practice
technique P, 1921
pre-image
definition PI, 1922
kernel
theorem KPI, 1923
pre-images
example SPIAS, 1924
principal axis theorem, 1925
product of triangular matrices
theorem PTMT, 1926
Property
AA, 1927
AAC, 1928
AACN, 1929
AAF, 1930
AAM, 1931
AC, 1932
ACC, 1933
ACCN, 1934
ACF, 1935
ACM, 1936
AI, 1937
AIC, 1938
AICN, 1939
AIF, 1940
AIM, 1941
C, 1942
CACN, 1943
CAF, 1944
CC, 1945
CM, 1946
CMCN, 1947
CMF, 1948
DCN, 1949
DF, 1950
DMAM, 1951
DSA, 1952
DSAC, 1953
DSAM, 1954
DVA, 1955
DVAC, 1956
MACN, 1957
MAF, 1958
MCCN, 1959
MCF, 1960
MICN, 1961
MIF, 1962
O, 1963
OC, 1964
OCN, 1965
OF, 1966
OM, 1967
SC, 1968
SCC, 1969
SCM, 1970
SMA, 1971
SMAC, 1972
SMAM, 1973
Z, 1974
ZC, 1975
ZCN, 1976
ZF, 1977
ZM, 1978
PSHS (example), 1979
PSHS (subsection, section LC), 1980
PSM (definition), 1981
PSM (section), 1982
PSM (subsection, section PSM), 1983
PSM (subsection, section SD), 1984
PSMSR (theorem), 1985
PSPHS (theorem), 1986
PSS (subsection, section SSLE), 1987
PSSD (theorem), 1988
PSSLS (theorem), 1989
PT (section), 1990
PTFP (example), 1991
PTM (example), 1992
PTMEE (example), 1993
PTMT (theorem), 1994
Q (archetype), 1995
R (acronyms, section JCF), 1996
R (archetype), 1997
R (chapter), 1998
range
full
example FRAN, 1999
isomorphic to column space
theorem RCSI, 2000
linear transformation
example RAO, 2001
notation, 2002
of a linear transformation
definition RLT, 2003
pre-image
theorem RPI, 2004
subspace
theorem RLTS, 2005
surjective linear transformation
theorem RSLT, 2006
via matrix representation
example RVMR, 2007
rank
computing
theorem CRN, 2008
linear transformation
definition ROLT, 2009
matrix
definition ROM, 2010
example RNM, 2011
notation, 2012, 2013
of transpose
example RRTI, 2014
square matrix
example RNSM, 2015
surjective linear transformation
theorem ROSLT, 2016
transpose
theorem RMRT, 2017
rank one decomposition
size 2
example ROD2, 2018
size 4
example ROD4, 2019
theorem ROD, 2020
rank+nullity
theorem RPNC, 2021
RAO (example), 2022
RCLS (theorem), 2023
RCSI (theorem), 2024
RD (subsection, section VS), 2025
RDS (theorem), 2026
READ (subsection, section B), 2027
READ (subsection, section CB), 2028
READ (subsection, section CRS), 2029
READ (subsection, section D), 2030
READ (subsection, section DM), 2031
READ (subsection, section EE), 2032
READ (subsection, section FS), 2033
READ (subsection, section HSE), 2034
READ (subsection, section ILT), 2035
READ (subsection, section IVLT), 2036
READ (subsection, section LC), 2037
READ (subsection, section LDS), 2038
READ (subsection, section LI), 2039
READ (subsection, section LISS), 2040
READ (subsection, section LT), 2041
READ (subsection, section MINM), 2042
READ (subsection, section MISLE), 2043
READ (subsection, section MM), 2044
READ (subsection, section MO), 2045
READ (subsection, section MR), 2046
READ (subsection, section NM), 2047
READ (subsection, section O), 2048
READ (subsection, section PD), 2049
READ (subsection, section PDM), 2050
READ (subsection, section PEE), 2051
READ (subsection, section RREF), 2052
READ (subsection, section S), 2053
READ (subsection, section SD), 2054
READ (subsection, section SLT), 2055
READ (subsection, section SS), 2056
READ (subsection, section SSLE), 2057
READ (subsection, section TSS), 2058
READ (subsection, section VO), 2059
READ (subsection, section VR), 2060
READ (subsection, section VS), 2061
READ (subsection, section WILA), 2062
reduced row-echelon form
analysis
notation, 2063
definition RREF, 2064
example NRREF, 2065
example RREF, 2066
extended
definition EEF, 2067
notation
example RREFN, 2068
unique
theorem RREFU, 2069
reducing a span
example RSC5, 2070
relation of linear dependence
definition RLD, 2071
definition RLDCV, 2072
REM (definition), 2073
REMEF (theorem), 2074
REMES (theorem), 2075
REMRS (theorem), 2076
RES (example), 2077
RGEN (theorem), 2078
RLD (definition), 2079
RLDCV (definition), 2080
RLT (definition), 2081
RLT (notation), 2082
RLT (subsection, section IS), 2083
RLT (subsection, section SLT), 2084
RLTS (theorem), 2085
RMRT (theorem), 2086
RNLT (subsection, section IVLT), 2087
RNM (example), 2088
RNM (subsection, section D), 2089
RNNM (subsection, section D), 2090
RNNM (theorem), 2091
RNSM (example), 2092
RO (definition), 2093
RO (notation), 2094
RO (subsection, section RREF), 2095
ROD (section), 2096
ROD (theorem), 2097
ROD2 (example), 2098
ROD4 (example), 2099
ROLT (definition), 2100
ROLT (notation), 2101
ROM (definition), 2102
ROM (notation), 2103
ROSLT (theorem), 2104
row operations
definition RO, 2105
elementary matrices, 2106, 2107
notation, 2108
row reduce
mathematica, 2109
ti83, 2110
ti86, 2111
row space
Archetype I
example RSAI, 2112
as column space, 2113
basis
example RSB, 2114
theorem BRS, 2115
matrix, 2116
notation, 2117
row-equivalent matrices
theorem REMRS, 2118
subspace
theorem RSMS, 2119
row-equivalent matrices
definition REM, 2120
example TREM, 2121
row space, 2122
row spaces
example RSREM, 2123
theorem REMES, 2124
row-reduce
the verb
definition RR, 2125
row-reduced matrices
theorem REMEF, 2126
RPI (theorem), 2127
RPNC (theorem), 2128
RPNDD (theorem), 2129
RR (definition), 2130
RR.MMA (computation, section MMA), 2131
RR.TI83 (computation, section TI83), 2132
RR.TI86 (computation, section TI86), 2133
RREF (definition), 2134
RREF (example), 2135
RREF (section), 2136
RREF (subsection, section RREF), 2137
RREFA (notation), 2138
RREFN (example), 2139
RREFU (theorem), 2140
RRTI (example), 2141
RS (example), 2142
RSAI (example), 2143
RSB (example), 2144
RSC5 (example), 2145
RSLT (theorem), 2146
RSM (definition), 2147
RSM (notation), 2148
RSM (subsection, section CRS), 2149
RSMS (theorem), 2150
RSNS (example), 2151
RSREM (example), 2152
RSSC4 (example), 2153
RT (subsection, section PD), 2154
RVMR (example), 2155
S (archetype), 2156
S (definition), 2157
S (example), 2158
S (section), 2159
SAA (example), 2160
SAB (example), 2161
SABMI (example), 2162
SAE (example), 2163
SAN (example), 2164
SAR (example), 2165
SAS (section), 2166
SAV (example), 2167
SC (definition), 2168
SC (example), 2169
SC (notation), 2170
SC (Property), 2171
SC (subsection, section S), 2172
SC (subsection, section SET), 2173
SC3 (example), 2174
SCAA (example), 2175
SCAB (example), 2176
SCAD (example), 2177
scalar closure
column vectors
Property SCC, 2178
matrices
Property SCM, 2179
vectors
Property SC, 2180
scalar multiple
matrix inverse, 2181
scalar multiplication
zero scalar
theorem ZSSM, 2182
zero vector
theorem ZVSM, 2183
zero vector result
theorem SMEZV, 2184
scalar multiplication associativity
column vectors
Property SMAC, 2185
matrices
Property SMAM, 2186
vectors
Property SMA, 2187
SCB (theorem), 2188
SCC (Property), 2189
SCM (Property), 2190
SD (section), 2191
SDS (example), 2192
SE (definition), 2193
SE (notation), 2194
secret sharing
6 ways
example SS6W, 2195
SEE (example), 2196
SEEF (example), 2197
SER (theorem), 2198
set
cardinality
definition C, 2199
example CS, 2200
notation, 2201
complement
definition SC, 2202
example SC, 2203
notation, 2204
definition SET, 2205
empty
definition ES, 2206
equality
definition SE, 2207
notation, 2208
intersection
definition SI, 2209
example SI, 2210
notation, 2211
membership
example SETM, 2212
notation, 2213
size, 2214
subset, 2215
union
definition SU, 2216
example SU, 2217
notation, 2218
SET (definition), 2219
SET (section), 2220
SETM (example), 2221
SETM (notation), 2222
shoes, 2223
SHS (subsection, section HSE), 2224
SI (definition), 2225
SI (example), 2226
SI (notation), 2227
SI (subsection, section IVLT), 2228
SIM (definition), 2229
similar matrices
equal eigenvalues
example EENS, 2230
eual eigenvalues
theorem SMEE, 2231
example SMS3, 2232
example SMS5, 2233
similarity
definition SIM, 2234
equivalence relation
theorem SER, 2235
singular matrix
Archetype A
example S, 2236
null space
example NSS, 2237
singular matrix, row-reduced
example SRR, 2238
singular value decomposition
theorem SVD, 2239
singular values
definition SV, 2240
SLE (acronyms, section NM), 2241
SLE (chapter), 2242
SLE (definition), 2243
SLE (subsection, section SSLE), 2244
SLELT (subsection, section IVLT), 2245
SLEMM (theorem), 2246
SLSLC (theorem), 2247
SLT (definition), 2248
SLT (section), 2249
SLTB (theorem), 2250
SLTD (subsection, section SLT), 2251
SLTD (theorem), 2252
SLTLT (theorem), 2253
SM (definition), 2254
SM (notation), 2255
SM (subsection, section SD), 2256
SM2Z7 (example), 2257
SM32 (example), 2258
SMA (Property), 2259
SMAC (Property), 2260
SMAM (Property), 2261
SMEE (theorem), 2262
SMEZV (theorem), 2263
SMLT (example), 2264
SMS (theorem), 2265
SMS3 (example), 2266
SMS5 (example), 2267
SMZD (theorem), 2268
SMZE (theorem), 2269
SNCM (theorem), 2270
SO (subsection, section SET), 2271
socks, 2272
SOL (subsection, section B), 2273
SOL (subsection, section CB), 2274
SOL (subsection, section CRS), 2275
SOL (subsection, section D), 2276
SOL (subsection, section DM), 2277
SOL (subsection, section EE), 2278
SOL (subsection, section F), 2279
SOL (subsection, section FS), 2280
SOL (subsection, section HSE), 2281
SOL (subsection, section ILT), 2282
SOL (subsection, section IVLT), 2283
SOL (subsection, section LC), 2284
SOL (subsection, section LDS), 2285
SOL (subsection, section LI), 2286
SOL (subsection, section LISS), 2287
SOL (subsection, section LT), 2288
SOL (subsection, section MINM), 2289
SOL (subsection, section MISLE), 2290
SOL (subsection, section MM), 2291
SOL (subsection, section MO), 2292
SOL (subsection, section MR), 2293
SOL (subsection, section NM), 2294
SOL (subsection, section PD), 2295
SOL (subsection, section PDM), 2296
SOL (subsection, section PEE), 2297
SOL (subsection, section RREF), 2298
SOL (subsection, section S), 2299
SOL (subsection, section SD), 2300
SOL (subsection, section SLT), 2301
SOL (subsection, section SS), 2302
SOL (subsection, section SSLE), 2303
SOL (subsection, section T), 2304
SOL (subsection, section TSS), 2305
SOL (subsection, section VO), 2306
SOL (subsection, section VR), 2307
SOL (subsection, section VS), 2308
SOL (subsection, section WILA), 2309
solution set
Archetype A
example SAA, 2310
archetype E
example SAE, 2311
theorem PSPHS, 2312
solution sets
possibilities
theorem PSSLS, 2313
solution vector
definition SOLV, 2314
SOLV (definition), 2315
solving homogeneous system
Archetype A
example HISAA, 2316
Archetype B
example HUSAB, 2317
Archetype D
example HISAD, 2318
solving nonlinear equations
example STNE, 2319
SP4 (example), 2320
span
basic
example ABS, 2321
basis
theorem BS, 2322
definition SS, 2323
definition SSCV, 2324
improved
example IAS, 2325
notation, 2326
reducing
example RSSC4, 2327
reduction
example RS, 2328
removing vectors
example COV, 2329
reworking elements
example RES, 2330
set of polynomials
example SSP, 2331
subspace
theorem SSS, 2332
span of columns
Archetype A
example SCAA, 2333
Archetype B
example SCAB, 2334
Archetype D
example SCAD, 2335
spanning set
crazy vector space
example SSC, 2336
definition TSVS, 2337
matrices
example SSM22, 2338
more vectors
theorem SSLD, 2339
polynomials
example SSP4, 2340
SPIAS (example), 2341
SQM (definition), 2342
square root
eigenvalues, eigenspaces
theorem EESR, 2343
matrix
definition SRM, 2344
notation, 2345
positive semi-definite matrix
theorem PSMSR, 2346
unique
theorem USR, 2347
SR (section), 2348
SRM (definition), 2349
SRM (notation), 2350
SRM (subsection, section SR), 2351
SRR (example), 2352
SS (definition), 2353
SS (example), 2354
SS (section), 2355
SS (subsection, section LISS), 2356
SS (theorem), 2357
SS6W (example), 2358
SSC (example), 2359
SSCV (definition), 2360
SSET (definition), 2361
SSET (example), 2362
SSET (notation), 2363
SSLD (theorem), 2364
SSLE (section), 2365
SSM22 (example), 2366
SSNS (example), 2367
SSNS (subsection, section SS), 2368
SSNS (theorem), 2369
SSP (example), 2370
SSP4 (example), 2371
SSRLT (theorem), 2372
SSS (theorem), 2373
SSSLT (subsection, section SLT), 2374
SSV (notation), 2375
SSV (subsection, section SS), 2376
standard unit vector
notation, 2377
starting proofs
technique GS, 2378
STLT (example), 2379
STNE (example), 2380
SU (definition), 2381
SU (example), 2382
SU (notation), 2383
submatrix
notation, 2384
subset
definition SSET, 2385
notation, 2386
subspace
as null space
example RSNS, 2387
characterized
example ASC, 2388
definition S, 2389
in
example SP4, 2390
not, additive closure
example NSC2A, 2391
not, scalar closure
example NSC2S, 2392
not, zero vector
example NSC2Z, 2393
testing
theorem TSS, 2394
trivial
definition TS, 2395
verification
example SC3, 2396
example SM32, 2397
subspaces
equal dimension
theorem EDYES, 2398
surjective
Archetype N
example SAN, 2399
example SAR, 2400
not
example NSAQ, 2401
example NSAQR, 2402
not, Archetype O
example NSAO, 2403
not, by dimension
example NSDAT, 2404
polynomials to matrices
example SAV, 2405
surjective linear transformation
bases
theorem SLTB, 2406
surjective linear transformations
dimension
theorem SLTD, 2407
SUV (definition), 2408
SUV (notation), 2409
SUVB (theorem), 2410
SUVOS (example), 2411
SV (definition), 2412
SVD (section), 2413
SVD (subsection, section SVD), 2414
SVD (theorem), 2415
SVP4 (example), 2416
SYM (definition), 2417
SYM (example), 2418
symmetric matrices
theorem SMS, 2419
symmetric matrix
example SYM, 2420
system of equations
vector equality
example VESE, 2421
system of linear equations
definition SLE, 2422
T (archetype), 2423
T (definition), 2424
T (notation), 2425
T (part), 2426
T (section), 2427
T (technique, section PT), 2428
TCSD (example), 2429
TD (section), 2430
TD (subsection, section TD), 2431
TD (theorem), 2432
TD4 (example), 2433
TDEE (theorem), 2434
TDEE6 (example), 2435
TDSSE (example), 2436
TDSSE (subsection, section TD), 2437
technique
C, 2438
CD, 2439
CP, 2440
CV, 2441
D, 2442
DC, 2443
E, 2444
GS, 2445
I, 2446
L, 2447
LC, 2448
ME, 2449
N, 2450
P, 2451
PI, 2452
T, 2453
U, 2454
theorem
AA, 2455
AIP, 2456
AISM, 2457
AIU, 2458
AMA, 2459
AMSM, 2460
BCS, 2461
BIS, 2462
BNS, 2463
BRS, 2464
BS, 2465
CB, 2466
CCM, 2467
CCRA, 2468
CCRM, 2469
CCT, 2470
CFDVS, 2471
CFNLT, 2472
CHT, 2473
CILTI, 2474
CINM, 2475
CIVLT, 2476
CLI, 2477
CLTLT, 2478
CMVEI, 2479
CNMB, 2480
COB, 2481
CPSM, 2482
CRMA, 2483
CRMSM, 2484
CRN, 2485
CRSM, 2486
CRVA, 2487
CSCS, 2488
CSLTS, 2489
CSMS, 2490
CSNM, 2491
CSRN, 2492
CSRST, 2493
CSS, 2494
CUMOS, 2495
DC, 2496
DCM, 2497
DCP, 2498
DEC, 2499
DED, 2500
DEM, 2501
DEMMM, 2502
DER, 2503
DERC, 2504
DFS, 2505
DGES, 2506
DIM, 2507
DLDS, 2508
DM, 2509
DMFE, 2510
DMHP, 2511
DMMP, 2512
DMST, 2513
DNLT, 2514
DP, 2515
DRCM, 2516
DRCMA, 2517
DRCS, 2518
DRMM, 2519
DSD, 2520
DSFB, 2521
DSFOS, 2522
DSLI, 2523
DSZI, 2524
DSZV, 2525
DT, 2526
DVM, 2527
DZRC, 2528
EDELI, 2529
EDYES, 2530
EEMAP, 2531
EER, 2532
EESR, 2533
EIM, 2534
EIS, 2535
ELIS, 2536
EMDRO, 2537
EMHE, 2538
EMMVP, 2539
EMN, 2540
EMNS, 2541
EMP, 2542
EMRCP, 2543
EMS, 2544
ENLT, 2545
EOMP, 2546
EOPSS, 2547
EPM, 2548
EPSM, 2549
ERMCP, 2550
ESMM, 2551
ETM, 2552
FIMP, 2553
FS, 2554
FTMR, 2555
FVCS, 2556
G, 2557
GEK, 2558
GESD, 2559
GESIS, 2560
GSP, 2561
HMIP, 2562
HMOE, 2563
HMRE, 2564
HMVEI, 2565
HPC, 2566
HPDAA, 2567
HPHI, 2568
HPHID, 2569
HPSMM, 2570
HSC, 2571
ICBM, 2572
ICLT, 2573
IFDVS, 2574
IILT, 2575
ILTB, 2576
ILTD, 2577
ILTIS, 2578
ILTLI, 2579
ILTLT, 2580
IMILT, 2581
IMR, 2582
IP, 2583
IPAC, 2584
IPN, 2585
IPSM, 2586
IPVA, 2587
ISRN, 2588
ITMT, 2589
IVSED, 2590
JCFLT, 2591
KILT, 2592
KLTS, 2593
KNSI, 2594
KPI, 2595
KPIS, 2596
KPLT, 2597
KPNLT, 2598
LIVHS, 2599
LIVRN, 2600
LNSMS, 2601
LSMR, 2602
LTDB, 2603
LTLC, 2604
LTTZZ, 2605
MBLT, 2606
MCT, 2607
ME, 2608
MIMI, 2609
MISM, 2610
MIT, 2611
MIU, 2612
MLTCV, 2613
MLTLT, 2614
MMA, 2615
MMAD, 2616
MMCC, 2617
MMDAA, 2618
MMIM, 2619
MMIP, 2620
MMSMM, 2621
MMT, 2622
MMZM, 2623
MNEM, 2624
MRCB, 2625
MRCLT, 2626
MRMLT, 2627
MRRGE, 2628
MRSLT, 2629
MVSLD, 2630
NEM, 2631
NI, 2632
NJB, 2633
NME1, 2634
NME2, 2635
NME3, 2636
NME4, 2637
NME5, 2638
NME6, 2639
NME7, 2640
NME8, 2641
NME9, 2642
NMLIC, 2643
NMPEM, 2644
NMRRI, 2645
NMTNS, 2646
NMUS, 2647
NOILT, 2648
NPNT, 2649
NSMS, 2650
NVM, 2651
OBNM, 2652
OBUTR, 2653
OD, 2654
OSIS, 2655
OSLI, 2656
PCNA, 2657
PDM, 2658
PEEF, 2659
PIP, 2660
PSMSR, 2661
PSPHS, 2662
PSSD, 2663
PSSLS, 2664
PTMT, 2665
RCLS, 2666
RCSI, 2667
RDS, 2668
REMEF, 2669
REMES, 2670
REMRS, 2671
RGEN, 2672
RLTS, 2673
RMRT, 2674
RNNM, 2675
ROD, 2676
ROSLT, 2677
RPI, 2678
RPNC, 2679
RPNDD, 2680
RREFU, 2681
RSLT, 2682
RSMS, 2683
SCB, 2684
SER, 2685
SLEMM, 2686
SLSLC, 2687
SLTB, 2688
SLTD, 2689
SLTLT, 2690
SMEE, 2691
SMEZV, 2692
SMS, 2693
SMZD, 2694
SMZE, 2695
SNCM, 2696
SS, 2697
SSLD, 2698
SSNS, 2699
SSRLT, 2700
SSS, 2701
SUVB, 2702
SVD, 2703
TD, 2704
TDEE, 2705
technique T, 2706
TIST, 2707
TL, 2708
TMA, 2709
TMSM, 2710
TSE, 2711
TSRM, 2712
TSS, 2713
TT, 2714
TTMI, 2715
UMCOB, 2716
UMI, 2717
UMPIP, 2718
USR, 2719
UTMR, 2720
VFSLS, 2721
VRI, 2722
VRILT, 2723
VRLT, 2724
VRRB, 2725
VRS, 2726
VSLT, 2727
VSPCV, 2728
VSPM, 2729
ZSSM, 2730
ZVSM, 2731
ZVU, 2732
ti83
matrix entry (computation), 2733
row reduce (computation), 2734
vector linear combinations (computation), 2735
TI83 (section), 2736
ti86
matrix entry (computation), 2737
row reduce (computation), 2738
transpose of a matrix (computation), 2739
vector linear combinations (computation), 2740
TI86 (section), 2741
TIS (example), 2742
TIST (theorem), 2743
TIVS (example), 2744
TKAP (example), 2745
TL (theorem), 2746
TLC (example), 2747
TM (definition), 2748
TM (example), 2749
TM (notation), 2750
TM (subsection, section OD), 2751
TM.MMA (computation, section MMA), 2752
TM.TI86 (computation, section TI86), 2753
TMA (theorem), 2754
TMP (example), 2755
TMSM (theorem), 2756
TOV (example), 2757
trace
definition T, 2758
linearity
theorem TL, 2759
matrix multiplication
theorem TSRM, 2760
notation, 2761
similarity
theorem TIST, 2762
sum of eigenvalues
theorem TSE, 2763
trail mix
example TMP, 2764
transpose
matrix scalar multiplication
theorem TMSM, 2765
example TM, 2766
matrix addition
theorem TMA, 2767
matrix inverse, 2768, 2769
notation, 2770
scalar multiplication, 2771
transpose of a matrix
mathematica, 2772
ti86, 2773
transpose of a transpose
theorem TT, 2774
TREM (example), 2775
triangular decomposition
entry by entry, size 6
example TDEE6, 2776
entry by entry
theorem TDEE, 2777
size 4
example TD4, 2778
solving systems of equations
example TDSSE, 2779
theorem TD, 2780
triangular matrix
inverse
theorem ITMT, 2781
trivial solution
system of equations
definition TSHSE, 2782
TS (definition), 2783
TS (subsection, section S), 2784
TSE (theorem), 2785
TSHSE (definition), 2786
TSM (subsection, section MO), 2787
TSRM (theorem), 2788
TSS (section), 2789
TSS (subsection, section S), 2790
TSS (theorem), 2791
TSVS (definition), 2792
TT (theorem), 2793
TTMI (theorem), 2794
TTS (example), 2795
typical systems,
example TTS, 2796
U (archetype), 2797
U (technique, section PT), 2798
UM (definition), 2799
UM (subsection, section MINM), 2800
UM3 (example), 2801
UMCOB (theorem), 2802
UMI (theorem), 2803
UMPIP (theorem), 2804
unique solution,
example US, 2805
example USR, 2806
uniqueness
technique U, 2807
unit vectors
basis
theorem SUVB, 2808
definition SUV, 2809
orthogonal
example SUVOS, 2810
unitary
permutation matrix
example UPM, 2811
size 3
example UM3, 2812
unitary matrices
columns
theorem CUMOS, 2813
unitary matrix
inner product
theorem UMPIP, 2814
UPM (example), 2815
upper triangular matrix
definition UTM, 2816
US (example), 2817
USR (example), 2818
USR (theorem), 2819
UTM (definition), 2820
UTMR (subsection, section OD), 2821
UTMR (theorem), 2822
V (acronyms, section O), 2823
V (archetype), 2824
V (chapter), 2825
VA (example), 2826
Vandermonde matrix
definition VM, 2827
vandermonde matrix
determinant
theorem DVM, 2828
nonsingular
theorem NVM, 2829
size 4
example VM4, 2830
VEASM (subsection, section VO), 2831
vector
addition
definition CVA, 2832
column
definition CV, 2833
equality
definition CVE, 2834
notation, 2835
inner product
definition IP, 2836
norm
definition NV, 2837
notation, 2838
of constants
definition VOC, 2839
product with matrix, 2840, 2841
scalar multiplication
definition CVSM, 2842
vector addition
example VA, 2843
vector component
notation, 2844
vector form of solutions
Archetype D
example VFSAD, 2845
Archetype I
example VFSAI, 2846
Archetype L
example VFSAL, 2847
example VFS, 2848
mathematica, 2849
theorem VFSLS, 2850
vector linear combinations
mathematica, 2851
ti83, 2852
ti86, 2853
vector representation
example AVR, 2854
example VRC4, 2855
injective
theorem VRI, 2856
invertible
theorem VRILT, 2857
linear transformation
definition VR, 2858
theorem VRLT, 2859
surjective
theorem VRS, 2860
theorem VRRB, 2861
vector representations
polynomials
example VRP2, 2862
vector scalar multiplication
example CVSM, 2863
vector space
characterization
theorem CFDVS, 2864
column vectors
definition VSCV, 2865
definition VS, 2866
infinite dimension
example VSPUD, 2867
linear transformations
theorem VSLT, 2868
over integers mod 5
example VSIM5, 2869
vector space of column vectors
notation, 2870
vector space of functions
example VSF, 2871
vector space of infinite sequences
example VSIS, 2872
vector space of matrices
definition VSM, 2873
example VSM, 2874
notation, 2875
vector space of polynomials
example VSP, 2876
vector space properties
column vectors
theorem VSPCV, 2877
matrices
theorem VSPM, 2878
vector space, crazy
example CVS, 2879
vector space, singleton
example VSS, 2880
vector spaces
isomorphic
definition IVS, 2881
theorem IFDVS, 2882
VESE (example), 2883
VFS (example), 2884
VFSAD (example), 2885
VFSAI (example), 2886
VFSAL (example), 2887
VFSLS (theorem), 2888
VFSS (subsection, section LC), 2889
VFSS.MMA (computation, section MMA), 2890
VLC.MMA (computation, section MMA), 2891
VLC.TI83 (computation, section TI83), 2892
VLC.TI86 (computation, section TI86), 2893
VM (definition), 2894
VM (section), 2895
VM4 (example), 2896
VO (section), 2897
VOC (definition), 2898
VR (definition), 2899
VR (section), 2900
VR (subsection, section LISS), 2901
VRC4 (example), 2902
VRI (theorem), 2903
VRILT (theorem), 2904
VRLT (theorem), 2905
VRP2 (example), 2906
VRRB (theorem), 2907
VRS (theorem), 2908
VS (acronyms, section PD), 2909
VS (chapter), 2910
VS (definition), 2911
VS (section), 2912
VS (subsection, section VS), 2913
VSCV (definition), 2914
VSCV (example), 2915
VSCV (notation), 2916
VSF (example), 2917
VSIM5 (example), 2918
VSIS (example), 2919
VSLT (theorem), 2920
VSM (definition), 2921
VSM (example), 2922
VSM (notation), 2923
VSP (example), 2924
VSP (subsection, section MO), 2925
VSP (subsection, section VO), 2926
VSP (subsection, section VS), 2927
VSPCV (theorem), 2928
VSPM (theorem), 2929
VSPUD (example), 2930
VSS (example), 2931
W (archetype), 2932
WILA (section), 2933
X (archetype), 2934
Z (Property), 2935
ZC (Property), 2936
ZCN (Property), 2937
ZCV (definition), 2938
ZCV (notation), 2939
zero
complex numbers
Property ZCN, 2940
field
Property ZF, 2941
zero column vector
definition ZCV, 2942
notation, 2943
zero matrix
notation, 2944
zero vector
column vectors
Property ZC, 2945
matrices
Property ZM, 2946
unique
theorem ZVU, 2947
vectors
Property Z, 2948
ZF (Property), 2949
ZM (definition), 2950
ZM (notation), 2951
ZM (Property), 2952
ZNDAB (example), 2953
ZSSM (theorem), 2954
ZVSM (theorem), 2955
ZVU (theorem), 2956