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| Авторизация |
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| Поиск по указателям |
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| Nicholson W.K. — Linear Algebra with Applications |
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| Предметный указатель |
Inner product 421
inner product of functions 422
Inner product of matrices 422
Inner product on C 303
Inner product on R 270 421
Inner product space 421
Inner product space, angle in 431
Inner product space, approximation theorem 438
Inner product space, axioms 421
Inner product space, Cauchy inequality 428
Inner product space, distance in 425
Inner product space, expansion theorem 433
Inner product space, Gram — Schmidt algorithm 434
Inner product space, length in 425
Inner product space, norm in 425
Inner product space, orthogonality 431
Inner product space, projection theorem 437
Inner product space, Pythagorean theorem 432
Inner product space, Schwarz inequality 427
Inner product space, triangle inequality 428
Input-output model 90
Input-output model, matrix 91
Interpolating polynomial 132
Intersection of subspaces 219 394
interval 192
Invariant subspace 388
Inverse algorithm for matrices 61
Inverse of a complex number 467
Inverse of a linear transformation 367
Inverse of a matrix 57 63 74 76
Inverse of a row operation 70 71
Inverse, generalized 325 331
Inverse, properties of 63
Invertible matrix 57
Involutions 397
Isometry 449
Isomorphic vector spaces 362
Isomorphism 362 367
Jacobi identity 177
Jordan block 408
Jordan canonical form 408
Jordan, C 408
Junction rule 27 29
Kcmeny, J. G 102 481
Kernel of a linear translormation 352
Kirchoff's laws 29
Lagrange identity 172
Lagrange interpolation 242 434
Lagrange polynomials 434
Lagrange, J. L 172
Lancaster, P 92
Laplace expansion 110 111 136
Laplace, P S 110
Law of Cosines 157 431
Law of Sines 177
Leading 1 11
Leading column 82
Leading variables 13
Least squares 178 327
Least squares, appproximation by other functions 330
Least squares, approximating line 179
Least squares, approximating polynomial 182 327
Legendre polynomials 436
Legendre, A M 436
Leontief, W 90
Level 483
Level, parametric equations 151
Level, slope 153
Level, symmetric form 155
Level, vector equation 151
Line 150
Line, direction vector 150
linear combination 204
Linear combination of solutions 55 203—204
Linear combination, trivial 209
Linear combination, unique representation as 212
Linear constraint 482 486 489
Linear dependence 209
Linear equations 1
Linear equations, associated homogeneous system 50
Linear equations, augmented matrix 5
Linear equations, coefficient matrix of 50
Linear equations, consistent 20
Linear equations, constant matnx of 50
Linear equations, elementary operations on 6
Linear equations, equivalent system 6
Linear equations, Gaussian elimination 10 13
Linear equations, homogeneous 24
Linear equations, inconsistent 20
Linear equations, leading vanables 13
Linear equations, matrix form 50
Linear equations, row-echelon form 11
Linear equations, solutions 2 50
Linear equations, trivial solutions 24
Linear function 486
Linear independence 209
Linear independence of matrix rows 235
Linear operator 339
Linear operator, characteristic polynomial 386
Linear operator, determinant 386
Linear operator, diagonalizablc 442
Linear operator, eigenspaces 392
Linear operator, eigenvalues 392
Linear operator, eigenvectors 392
Linear operator, idempotents 401
Linear operator, invariant subspace of 388
Linear operator, involutions 397
Linear operator, isometries 449
Linear operator, matrix of 382
Linear operator, orthogonal diagonalization 445
Linear operator, principle axes theorem 445
Linear operator, projection 448
Linear operator, reducible 397
Linear operator, restriction 389
Linear operator, shift 417
Linear operator, skew-symmetric 448
Linear operator, symmetric 444
Linear operator, trace 386
Linear programming 481
Linear programming, basic columns 491 495
Linear programming, basic feasible solution 491 495
Linear programming, basic variables 491 495
Linear programming, bounding hyperplane 486
Linear programming, comer point 486
Linear programming, constraints 482 486 489
Linear programming, degeneration 499
Linear programming, departing variable 493
Linear programming, entering variable 492
Linear programming, extreme point 486
Linear programming, feasible region 482 486
Linear programming, flow chart 496
Linear programming, graphical method 481
Linear programming, objective function 482 486 489
Linear programming, optimal solutions 492
Linear programming, pivot 492
Linear programming, simplex algorithm 496
Linear programming, simplex tableau 495
Linear programming, slack variables 490
Linear programming, standard problem 489
Linear programming, unbounded 494
Linear recurrence relation 267 411
Linear recurrence relation, associated polynomial 414
Linear recurrence relation, length of 412
Linear recurrence relation, space of solutions 411
Linear transformations 339
Linear transformations, action of 346
Linear transformations, addition 379
Linear transformations, composition 365
Linear transformations, compression 342
Linear transformations, contraction 351
| Linear transformations, dilation 351
Linear transformations, dimension theorem 357
Linear transformations, equality of 346
Linear transformations, evaluation map 352 359
Linear transformations, expansion 342
Linear transformations, identity transformation 343
Linear transformations, image 351 352
Linear transformations, inverse 367
Linear transformations, isomorphism 362 167 449
Linear transformations, matrix of 373 382
Linear transformations, matrix transformation 341
Linear transformations, null space 353
Linear transformations, nullity 354
Linear transformations, one-to-one 355
Linear transformations, onto 355
Linear transformations, preimage 351
Linear transformations, projection 349 351
Linear transformations, range 353
Linear transformations, rank 354
Linear transformations, reflection 343 349 458
Linear transformations, rotation 343 349 458
Linear transformations, scalar multiple 379
Linear transformations, scalar transformation 343
Linear transformations, shear 342
Linear transformations, standard matrix ol 349
Linear transformations, sum 379
Linear transformations, translation 351
Linear transformations, vector space of 379
Linear transformations, zero transformation 143
Linearly dependent 209
Linearly independent 209
Lower triangular matrix 78 117
Lower triangular matrix, block 118
LP-factorization 295
LU-factorization 80
LU-factorization, algorithm 82
LU-factorization, magnitude 141
LU-factorization, main diagonal 34 78
LU-factorization, Markov chain 96
LU-factorization, mathematical induction 501 502
LU-factorization, regular transition matrix 102
LU-factorization, stages 96 98
LU-factorization, stales 96 98
LU-factorization, state vectors 99
LU-factorization, steady-state \ector 102
LU-factorization, stochastic matrix 99
LU-factorization, transition matrix 98
LU-factorization, transition probability 96 98
Lucas sequence 419
Matnx computations with 55
Matnx computations with space of (null space) 200
Matnx computations with trivial 26
Matrix 5 33
Matrix form 50
Matrix of a linear transformation 373 382
Matrix, addition 35
Matrix, adjoint 108 123
Matrix, algebra 33
Matrix, augmented 5
Matrix, block diagonal 67
Matrix, block multiplication 52
Matrix, block triangular 78 391
Matrix, cancellation 64
Matrix, change of basis matrix 380
Matrix, characteristic polynomial 253 306
Matrix, Cholesky decomposition of 290
Matrix, cigcnspace 252
Matrix, coefficient 5 50
Matrix, cofactor 123
Matrix, column spacc 228
Matrix, columns 34
Matrix, commuting 45
Matrix, companion 120
Matrix, complcx 304
Matrix, congruent 320
Matrix, conjugate 304
Matrix, conjugate transpose 304
Matrix, constant 5 50
Matrix, demand 93
Matrix, determinant of 110
Matrix, diagonal 43 56
Matrix, diagonalization 261 262
Matrix, difference 36 193
Matrix, doubly stochastic 105
Matrix, eigenvalue 251
Matrix, eigenvector 251
Matrix, elementary 68
Matrix, elementary column operations 78
Matrix, elementary row operations 8 68
Matrix, entries 33
Matrix, equality 35
Matrix, equivalent 238
Matrix, form of linear equations 50
Matrix, generalized inverse 325
Matrix, hermitian 305
Matrix, Householder 301
Matrix, idempotent 56 68
Matrix, identity 45
Matrix, input-output 91
Matrix, inverse 57 63 74 76
Matrix, inversion algorithm 61
Matrix, invertible 57
Matrix, leading column 82
Matrix, lower triangular 78
Matrix, main diagonal 34 78
Matrix, minor 109
Matrix, Moore — Penrose inverse 331
Matrix, multiplication 43
Matrix, negative 36
Matrix, nilpotent 260
Matrix, normal 310
Matrix, null spacc 200
Matrix, orthogonal 282
Matrix, orthogonal diagonalization of 283
Matrix, orthogonally similar 288
Matrix, partition into blocks 52
Matrix, permutation 85 288 387
Matrix, PLU-factonzation of 86
Matrix, positive definite 289 293
Matrix, product 44
Matrix, projection matnx 281 288
Matrix, range of 200
Matrix, rank of 21 230
Matrix, rank theorem lor 229
Matrix, reduced row-echelon 11
Matrix, row equivalent 77
Matrix, row spacc of 228
Matrix, row-echelon 11
Matrix, rows 34
Matrix, scalar 105
Matrix, scalar multiple ol 38
Matrix, similar 256 383
Matrix, size 34 38
Matrix, skew — Hcrmitian 312
Matrix, skew-symmetric 43
Matrix, spcctrum of 284
Matrix, square 34
Matrix, standard 349
Matrix, stochastic 91 99
Matrix, submatrix 218
Matrix, sum 35
Matrix, symmetric 42 256
Matrix, tnangulation theorem 287
Matrix, trace of 56 257
Matrix, transformation 141
Matrix, transition (Markov chain) 98
Matrix, transpose 41
Matrix, triangular 78 117
Matrix, unitAriangulur 90
Matrix, unitary 307
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