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| Beezer R.A. — A First Course in Linear Algebra |
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| Предметный указатель |
A (appendix) 699
A (archetype) 703
A (definition) 194
A (notation) 194
A (part) 845
AA (Property) 285
AA (subsection, section WILA) 4
AA (theorem) 194
AAC (Property) 90
AACN (Property) 680
AAF (Property) 789
AALC (example) 97
AAM (Property) 189
ABLC (example) 96
ABS (example) 117
AC (Property) 285
ACC (Property) 90
ACCN (Property) 680
ACF (Property) 789
ACM (Property) 189
ACN (example) 679
Additive associativity, column vectors, Property AAC 90
Additive associativity, complex numbers, Property AACN 680
Additive associativity, matrices, Property AAM 189
Additive Associativity, vectors, Property AA 285
Additive commutativity, complex numbers, Property CACN 680
Additive inverse, complex numbers, Property AICN 681
Additive inverse, from scalar multiplication, theorem AISM 293
Additive inverses, column vectors, Property AIC 90
Additive inverses, matrices, Property AIM 189
Additive inverses, unique, theorem AIU 292
Additive inverses, vectors, Property AI 286
Addtive closure, column vectors, Property ACC 90
Addtive closure, complex numbers, Property ACCN 680
Addtive closure, field, Property ACF 789
Addtive closure, matrices, Property ACM 189
Addtive closure, vectors, Property AC 285
Adjoint, definition A 194
Adjoint, inner product, theorem AIP 209
Adjoint, notation 194
Adjoint, of a matrix sum, theorem AMA 194
Adjoint, of an adjoint, theorem AA 194
Adjoint, of matrix scalar multiplication, theorem AMSM 194
AHSAC (example) 63
AI (Property) 286
AIC (Property) 90
AICN (Property) 681
AIF (Property) 790
AIM (Property) 189
AIP (theorem) 209
AISM (theorem) 293
AIU (theorem) 292
AIVLT (example) 513
ALT (example) 458
ALTMM (example) 551
AM (definition) 28
AM (example) 25
AM (notation) 28
AM (subsection, section MO) 193
AMA (theorem) 194
AMAA (example) 28
AME (definition) 411
AMSM (theorem) 194
ANILT (example) 514
ANM (example) 608
AOS (example) 177
Archetype A, augmented matrix, example AMAA 28
Archetype A, column space 244
Archetype A, linearly dependent columns 142
Archetype A, singular matrix 73
Archetype A, solving homogeneous system 64
Archetype A, system as linear combination 97
Archetype B, column space 244
Archetype B, inverse, example CMIAB 221
Archetype B, linearly independent columns 142
Archetype B, nonsingular matrix 74
Archetype B, not invertible, example MWIAA 216
Archetype B, solutions via inverse, example SABMI 215
Archetype B, solutions, example SAB 36
Archetype B, solving homogeneous system 63
Archetype B, system as linear combination 96
Archetype B, vector equality 88
Archetype C, homogeneous system 63
Archetype D, column space, original columns 243
Archetype D, solving homogeneous system 64
Archetype D, vector form of solutions 99
Archetype I, column space from row operations 250
Archetype I, null space 65
Archetype I, row space 246
Archetype I, vector form of solutions 106
Archetype L, casting out vectors 159
Archetype L, null space span, linearly independent 145
Archetype L, vector form of solutions 108
ASC (example) 540
Augmented matrix, notation 28
AVR (example) 323
B (archetype) 707
B (definition) 331
B (section) 331
B (subsection, section B) 331
Basis, columns nonsingular matrix, example CABAK 336
Basis, common size, theorem BIS 348
Basis, crazy vector apace, example BC 334
Basis, definition B 331
Basis, matrices, example BM 332
Basis, matrices, example BSM22 333
Basis, polynomials, example BP 332
Basis, polynomials, example BPR 360
Basis, polynomials, example BSP4 332
Basis, polynomials, example SVP4 361
Basis, subspace of matrices, example BDM22 361
BC (example) 334
BCS (theorem) 242
BDE (example) 426
BDM22 (example) 361
Best cities, money magazine, example MBC 200
BIS (theorem) 348
BM (example) 332
BNM (subsection, section B) 336
BNS (theorem) 144
BP (example) 332
BPR (example) 360
BRLT (example) 505
BRS (theorem) 248
BS (theorem) 162
BSCV (subsection, section B) 334
BSM22 (example) 333
BSP4 (example) 332
C (archetype) 712
C (definition) 684
C (notation) 684
C (part) 3
C (Property) 285
C (technique, section PT) 689
CABAK (example) 336
CACN (Property) 680
CAEHW (example) 406
CAF (Property) 789
Canonical form, nilpotent linear transformation, example CFNLT 626
Canonical form, nilpotent linear transformation, theorem CFNLT 622
CAV (subsection, section O) 171
Cayley — Hamilton, theorem CHT 667
CB (section) 577
CB (theorem) 578
CBCV (example) 582
CBM (definition) 578
CBM (subsection, section CB) 578
CBP (example) 579
CC (Property) 90
CCCV (definition) 171
| CCCV (notation) 171
CCM (definition) 192
CCM (example) 192
CCM (notation) 192
CCM (theorem) 193
CCN (definition) 681
CCN (notation) 681
CCN (subsection, section CNO) 681
CCRA (theorem) 681
CCRM (theorem) 681
CCT (theorem) 682
CD (subsection, section DM) 381
CD (technique, section PT) 691
CEE (subsection, section EE) 407
CELT (example) 594
CELT (subsection, section CB) 589
CEMS6 413
CEMS6 (example) 413
CF (section) 845
CFDVS (theorem) 540
CFNLT (example) 626
CFNLT (subsection, section NLT) 622
CFNLT (theorem) 622
CFV (example) 56
Change of basis, between polynomials, example CBP 579
Change-of-basis matrix, definition CBM 578
Change-of-basis matrix, inverse, theorem ICBM 579
Change-of-basis, between column vectors, example CBCV 582
Change-of-basis, matrix representation, theorem MRCB 583
Change-of-basis, similarity, theorem SCB 586
Change-of-basis, theorem CB 578
Characteristic polynomial, definition CP 408
Characteristic polynomial, degree, theorem DCP 428
Characteristic polynomial, size 3 matrix, example CPMS3 408
CHT (subsection, section JCF) 667
CHT (theorem) 667
CILT (subsection, section ILT) 490
CILTI (theorem) 490
CIM (subsection, section MISLE) 217
CINM (theorem) 220
CIVLT (example) 517
CIVLT (theorem) 519
CLI (theorem) 541
CLTLT (theorem) 474
CM (definition) 26
CM (Property) 189
CM32 (example) 543
CMCN (Property) 680
CMF (Property) 789
CMI (example) 219
CMIAB (example) 221
CMVEI (theorem) 57
CN (appendix) 671
CNA (definition) 680
CNA (notation) 680
CNA (subsection, section CNO) 679
CNE (definition) 680
CNE (notation) 680
CNM (definition) 680
CNM (notation) 680
CNMB (theorem) 336
CNO (section) 679
CNS1 (example) 66
CNS2 (example) 66
CNSV (example) 175
COB (theorem) 337
Coefficient matrix, definition CM 26
Coefficient matrix, nonsingular, theorem SNCM 232
Column space, Archetype A, example CSAA 244
Column space, Archetype B, example CSAB 244
Column space, as null space, Archetype G, example FSAG 273
Column space, as null space, example CSANS 262
Column space, as null space, theorem FS 267
Column space, as row space, theorem CSRST 250
Column space, basis, theorem BCS 242
Column space, consistent system, theorem CSCS 240
Column space, consistent systems, example CSMCS 239
Column space, isomorphic to range 560
Column space, matrix 239
Column space, nonsingular matrix, theorem CSNM 245
Column space, notation 239
Column space, original columns, Archetype D, example CSOCD 243
Column space, row operations, Archetype I, example CSROI 250
Column space, subspace, theorem CSMS 309
Column space, testing membership, example MCSM 240
Column space, two Computations, example CSTW 242
Column vector addition, notation 88
Column vector scalar multiplication, notation 89
Commutativity, column vectors, Property CC 90
Commutativity, matrices, Property CM 189
Commutativity, vectors, Property C 285
Complex arithmetic, example ACN 679
Complex m-space, example VSCV 287
Complex number, conjugate, definition CCN 681
Complex number, conjugate, example CSCN 681
Complex number, modulus, definition MCN 682
Complex number, modulus, example MSCN 682
Complex numbers, addition, definition CNA 680
Complex numbers, addition, notation 680
Complex numbers, arithmetic properties, theorem PCNA 680
Complex numbers, equality, definition CNE 680
Complex numbers, equality, notation 680
Complex numbers, multiplication, definition CNM 680
Complex numbers, multiplication, notation 680
Complex vector space, dimension, theorem DCM 349
Composition, injective linear transformations, theorem CILTI 490
Composition, surjective linear transformations, theorem CSLTS 507
Conjugate of a vector, notation 171
Conjugate, addition, theorem CCRA 681
Conjugate, column vector, definition CCCV 171
Conjugate, matrix, definition CCM 192
Conjugate, matrix, notation 192
Conjugate, multiplication, theorem CCRM 681
Conjugate, notation 681
Conjugate, of conjugate of a matrix, theorem CCM 193
Conjugate, scalar multiplication, theorem CRSM 171
Conjugate, twice, theorem CCT 682
Conjugate, vector addition, theorem CRVA 171
Conjugation, matrix addition, theorem CRMA 192
Conjugation, matrix scalar multiplication, theorem CRMSM 193
Conjugation, matrix transpose, theorem MCT 193
Consistent linear system 54
Consistent linear systems, theorem CSR.N 55
Consistent system, definition CS 51
Constructive proofs, technique C 689
Contradiction, technique CD 691
Contrapositive, technique CP 691
Converse, technique CV 691
Coordinates, orthonormal basis, theorem COB 337
Coordinatization principle 543
Coordinatization, linear combination of matrices, example CM32 543
Coordinatization, linear independence, theorem CLI 541
Coordinatization, orthonormal basis, example CROB3 339
Coordinatization, orthonormal basis, example CROB4 338
Coordinatization, spanning sets, theorem CSS 541
Coordinatizing, polynomials, example CP2 542
COV (example) 159
COV (subsection, section LDS) 159
CP (definition) 408
CP (subsection, section VR) 541
CP (technique, section PT) 691
CP2 (example) 542
CPMS3 (example) 408
CPSM (theorem) 813
Crazy vector space, example CVSR 540
Crazy vector space, properties, example PCVS 293
CRMA (theorem) 192
CRMSM (theorem) 193
CRN (theorem) 351
CROB3 (example) 339
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