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| Beezer R.A. — A First Course in Linear Algebra |
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| Предметный указатель |
IDV (definition) 53
IE (definition) 644
IE (notation) 644
IFDVS (theorem) 540
IILT (theorem) 516
ILT (definition) 481
ILT (figure) 483
ILT (section) 481
ILTB (theorem) 489
ILTD (subsection, section ILT) 490
ILTD (theorem) 490
ILTIS (theorem) 516
ILTLI (subsection, section ILT) 489
ILTLI (theorem) 489
ILTLT (theorem) 515
ILTVR (example) 562
IM (definition) 74
IM (example) 74
IM (notation) 74
IM (subsection, section MISLE) 216
IM11 (example) 790
IMILT (theorem) 564
IMP (definition) 790
IMR (theorem) 562
Inconsistent linear systems, theorem ISRN 55
Independent, dependent variables, definition IDV 53
Index, eigenvalue, definition IE 644
Index, eigenvalue, notation 644
Indexstring, example SM2Z7 791
Indexstring, example SSET 683
Indexstring, theorem DRCMA 389
Indexstring, theorem OBUTR 607
Indexstring, theorem UMCOB 340
Induction, technique I 694
Infinite solution set, example ISSI 52
Infinite solutions,  , example IS 17
Injective linear transformation, bases, theorem ILTB 489
Injective linear transformations, dimension, theorem ILTD 490
Injective, example IAP 488
Injective, example IAR 482
Injective, not, by dimension, example NIDAU 490
Injective, not, example NIAO 488
Injective, not, example NIAQ 481
Injective, not, example NIAQR 488
Injective, polynomials to matrices, example IAV 483
Inner product, anti-commutative, theorem IPAC 174
Inner product, example CSIP 172
Inner product, norm, theorem IPN 175
Inner product, notation 172
Inner product, positive, theorem PIP 176
Inner product, scalar multiplication, theorem IPSM 173
Inner product, vector addition, theorem IPVA 173
Integers, mod 11, example IM11 790
Integers, mod p, definition IMP 790
Integers, mod p, field, theorem FIMP 790
Interpolating polynomial, theorem IP 845
Invariant subspace, definition IS 631
Invariant subspace, eigenspace 632
Invariant subspace, eigenspaces, example EIS 633
Invariant subspace, example TIS 631
Invariant subspace, Jordan block, example ISJB 634
Invariant subspace, kernels of powers, theorem KPIS 633
Inverse, composition of linear transformations, theorem ICLT 519
Inverse, example CMI 219
Inverse, example MI 217
Inverse, notation 216
Inverse, of a matrix 216
Invertible linear transformation, defined by invertible matrix, theorem IMILT 564
Invertible linear transformations, composition, theorem CIVLT 519
Invertible linear transformations, computing, example CIVLT 517
IP (definition) 172
IP (notation) 172
IP (subsection, section O) 172
IP (theorem) 845
IPAC (theorem) 174
IPN (theorem) 175
IPSM (theorem) 173
IPVA (theorem) 173
IS (definition) 631
IS (example) 17
IS (section) 631
IS (subsection, section IS) 631
ISJB (example) 634
ISMR4 (example) 641
ISMR6 (example) 642
Isomorphic vector spaces, dimension, theorem IVSED 521
Isomorphic vector spaces, example TIVS 540
Isomorphic, multiple vector spaces, example MIVS 541
Isomorphic, vector spaces, example IVSAV 520
ISRN (theorem) 55
ISSI (example) 52
ITMT (theorem) 604
IV (subsection, section IVLT) 516
IVLT (definition) 513
IVLT (section) 513
IVLT (subsection, section IVLT) 513
IVLT (subsection, section MR) 562
IVS (definition) 520
IVSAV (example) 520
IVSED (theorem) 521
J (archetype) 740
JB (definition) 615
JB (notation) 615
JB4 (example) 615
JCF (definition) 655
JCF (section) 649
JCF (subsection, section JCF) 655
JCF10 (example) 656
JCFLT (theorem) 655
Jordan block, definition JB 615
Jordan block, nilpotent, theorem NJB 617
Jordan block, notation 615
Jordan block, size 4, example JB4 615
Jordan canonical form, definition JCF 655
Jordan canonical form, size 10, example JCF10 656
K (archetype) 745
Kernel, injective linear transformation, theorem KILT 487
Kernel, isomorphic to null space, theorem KNSI 557
Kernel, linear transformation, example NKAO 485
Kernel, notation 485
Kernel, of a linear transformation, definition KLT 485
Kernel, pre-image 487
Kernel, subspace, theorem KLTS 486
Kernel, trivial, example TKAP 486
Kernel, via matrix representation, example KVMR 558
KILT (theorem) 487
KLT (definition) 485
KLT (notation) 485
KLT (subsection, section ILT) 484
KLTS (theorem) 486
KNSI (theorem) 557
KPI (theorem) 487
KPIS (theorem) 633
KPLT (theorem) 619
KPNLT (example) 620
KPNLT (theorem) 620
KVMR (example) 558
L (archetype) 749
L (technique, section PT) 688
LA (subsection, section WILA) 3
LC (definition) 304
LC (section) 95
LC (subsection, section LC) 95
LC (technique, section PT) 695
LCCV (definition) 95
LCM (example) 304
LDCAA (example) 142
LDHS (example) 140
LDP4 (example) 348
LDRN (example) 141
| LDS (example) 137
LDS (section) 157
LDSS (subsection, section LDS) 157
Least squares solution, definition LSS 846
Least squares, minimizes residuals, theorem LSMR 846
Left null space, as row space 267
Left null space, definition LNS 261
Left null space, example LNS 261
Left null space, notation 261
Left null space, subspace, theorem LNSMS 309
Lemma, technique LC 695
LI (definition) 315
LI (section) 137
LI (subsection, section LISS) 315
LIC (example) 318
LICAB (example) 142
LICV (definition) 137
LIHS (example) 139
LIM32 (example) 317
Linear combination, definition LC 304
Linear combination, definition LCCV 95
Linear combination, example TLC 95
Linear combination, linear transformation 466
Linear combination, matrices, example LCM 304
Linear combination, system of equations, example AALC 97
Linear combination, system of equations, example ABLC 96
Linear combinations, solutions to linear systems, theorem SLSLC 98
Linear dependence, more vectors than size, theorem MVSLD 142
Linear independence, definition LI 315
Linear independence, definition LICV 137
Linear independence, homogeneous systems, theorem LIVHS 139
Linear independence, injective linear transformation, theorem ILTLI 489
Linear independence, matrices, example LIM32 317
Linear independence, orthogonal 178
Linear independence, r and n, theorem LIVRN 141
Linear solve, mathematica 671
Linear system, consistent, theorem RCLS 54
Linear system, matrix representation, definition LSMR 27
Linear system, matrix representation, notation 27
Linear systems, notation, example MNSLE 200
Linear systems, notation, example NSLE 27
Linear transformation inverse, via matrix representation, example ILTVR 562
Linear transformation restriction, on generalized eigenspace, example LTRGE 639
Linear transformation, addition, definition LTA 471
Linear transformation, addition, theorem MLTLT 472
Linear transformation, addition, theorem SLTLT 471
Linear transformation, as matrix multiplication, example ALTMM 551
Linear transformation, basis of range, example BRLT 505
Linear transformation, checking, example ALT 458
Linear transformation, composition, definition LTC 473
Linear transformation, composition, theorem CLTLT 474
Linear transformation, defined by a matrix, example LTM 462
Linear transformation, defined on a basis, example LTDB1 467
Linear transformation, defined on a basis, example LTDB2 468
Linear transformation, defined on a basis, example LTDB3 469
Linear transformation, defined on a basis, theorem LTDB 466
Linear transformation, definition LT 457
Linear transformation, identity, definition IDLT 513
Linear transformation, injection, definition ILT 481
Linear transformation, inverse of inverse, theorem IILT 516
Linear transformation, inverse, theorem ILTLT 515
Linear transformation, invertible, definition IVLT 513
Linear transformation, invertible, example AIVLT 513
Linear transformation, invertible, injective and surjective, theorem ILTIS 516
Linear transformation, Jordan canonical form, theorem JCFLT 655
Linear transformation, kernels of powers, theorem KPLT 619
Linear transformation, linear combination, theorem LTLC 466
Linear transformation, matrix of 464
Linear transformation, matrix of, example MFLT 464
Linear transformation, matrix of, example MOLT 465
Linear transformation, not invertible, example ANILT 514
Linear transformation, not, example NLT 459
Linear transformation, notation 457
Linear transformation, polynomials to matrices, example LTPM 460
Linear transformation, polynomials to polynomials, example LTPP 460
Linear transformation, rank plus nullity, theorem RPNDD 522
Linear transformation, restriction, definition LTR 638
Linear transformation, restriction, notation 639
Linear transformation, scalar multiple, example SMLT 473
Linear transformation, scalar multiplication, definition LTSM 472
Linear transformation, spanning range, theorem SSRLT 505
Linear transformation, sum, example STLT 472
Linear transformation, surjection, definition SLT 497
Linear transformation, vector space of 473
Linear transformation, zero vector, theorem LTTZZ 461
Linear transformations, compositions, example CTLT 474
Linear transformations, from matrices, theorem MBLT 463
Linearly dependent columns, Archetype A, example LDCAA 142
Linearly dependent set, example LDS 137
Linearly dependent set, linear combinations within theorem DLDS 157
Linearly dependent set, polynomials, example LDP4 348
Linearly dependent, r < n, example LDRN 141
Linearly dependent, via homogeneous system, example LDHS 140
Linearly independent columns, Archetype B, example LICAB 142
Linearly independent set, example LIS 138
Linearly independent set, example LLDS 141
Linearly independent, crazy vector space, example LIC 318
Linearly independent, extending sets, theorem ELIS 359
Linearly independent, polynomials, example LIP4 315
Linearly independent, via homogeneous system, example LIHS 139
LINM (subsection, section LI) 142
LINSB (example) 143
LIP4 (example) 315
LIS (example) 138
LISS (section) 315
LISV (subsection, section LI) 137
LIVHS (theorem) 139
LIVRN (theorem) 141
LLDS (example) 141
LNS (definition) 261
LNS (example) 261
LNS (notation) 261
LNS (subsection, section FS) 261
LNSMS (theorem) 309
Lower triangular matrix, definition LTM 603
LS.MMA (computation, section MMA) 671
LSMR (definition) 27
LSMR (notation) 27
LSMR (theorem) 846
LSS (definition) 846
LT (acronyms, section IVLT) 533
LT (chapter) 457
LT (definition) 457
LT (notation) 457
LT (section) 457
LT (subsection, section LT) 457
LTA (definition) 471
LTC (definition) 473
LTC (subsection, section LT) 461
LTDB (theorem) 466
LTDB1 (example) 467
LTDB2 (example) 468
LTDB3 (example) 469
LTLC (subsection, section LT) 466
LTLC (theorem) 466
LTM (definition) 603
LTM (example) 462
LTPM (example) 460
LTPP (example) 460
LTR (definition) 638
LTR (notation) 639
LTRGE (example) 639
LTSM (definition) 472
LTTZZ (theorem) 461
M (acronyms, section FS) 283
M (archetype) 752
M (chapter) 187
M (definition) 25
M (notation) 25
MA (definition) 187
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