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| Авторизация |
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| Carl D. Meyer — Matrix Analysis and Applied Linear Algebra Book and Solutions Manual |
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| Предметный указатель |
Distributive property of matrix multiplication 105
Distributive property of scalar multiplication 83
Domain 89
Doubly stochastic 702
Drazin generalized inverse 399 401 422 640
Drazin generalized inverse, Cauchy formula 615
Drazin generalized inverse, integral representation 441
Drazin, M.P. 399
Duffin, R.J. 441
Duncan, W.J. 124
Eckart, C. 411
Economic input—output model 681
Edge matrix 331
Edges 202
Eigenpair 490
Eigenspace 490
Eigenvalues 266 410 490
Eigenvalues of bordered matrices 552
Eigenvalues of discrete Laplacian 566 598
Eigenvalues of triangular and diagonal matrices 501
Eigenvalues of tridiagonal Toeplitz matrices 514
Eigenvalues, bounds for 498
Eigenvalues, continuity of 497
Eigenvalues, determinant and trace 494
Eigenvalues, distinct 514
Eigenvalues, generalized 571
Eigenvalues, index of 401 587 596
Eigenvalues, perturbations and condition of 528 551
Eigenvalues, semisimple 596
Eigenvalues, sensitivity, hermitian matrices 552
Eigenvalues, unit 696
Eigenvectors 266 490
Eigenvectors of commuting matrices 503
Eigenvectors of tridiagonal Toeplitz matrices 514
Eigenvectors, generalized 593 594
Eigenvectors, independent 511
electrical circuits 73 204
Elementary matrices 131—133
Elementary matrices, interchange matrices 135 140
Elementary orthogonal projector 322 431
Elementary orthogonal projector, rank of 337
Elementary reflector 324 444
Elementary reflector, determinant of 485
Elementary row and column operations 4 8
Elementary row and column operations, and determinants 463
Elementary triangular matrix 142
Ellipsoid 414
Ellipsoid, degenerate 425
Elliptical inner product 286
Elliptical norm 288
Empty set 383
EP matrices 408
Equal matrices 81
Equivalence, row and column 134
Equivalence, row and column, testing for 137
Equivalent norms, matrices 425
Equivalent norms, vectors 276
Equivalent statements 54
Equivalent systems 3
Ergodic class 695
Error, absolute and relative 414
Essentially positive matrix 686
Estimators 446
Euclidean norm 270
Euclidean norm, unitary invariance of 321
Evolutionary processes 616
Exponential complex 544
Exponential discrete 361
Exponential matrix 441 525
Exponential matrix, inverse of 614
Exponential matrix, products of 539
Exponential matrix, sums of 614
Extending to a basis 201
Extending to an orthonormal basis 325 335 338 404
Extension set 188
Faddeev and Sominskii 504
Fail-safe system 701
Fast Fourier transform (FFT) 368
Fast Fourier transform (FFT), FFT algorithm 368 370 373 381 651
Fast Fourier transform (FFT), FFT operation count 377
Fast integer multiplication 375
Filtering random noise 418
Finite difference matrix 522 639
Finite group 676
Finite-dimensional spaces 195
Fischer, Ernst 550
Five-point difference equations 564
Fixed points 386 391
Fixed points of a reflector 338
Flatness 164
Floating-point number 21
Forward substitution 145
Four fundamental subspaces 169
Four fundamental subspaces, summary 178
Fourier coefficients 299
Fourier expansion 299
Fourier expansion and projection 440
Fourier matrix 357
Fourier series 299 300
Fourier transform, continuous 357
Fourier transform, discrete 356 358
Fourier, Jean Baptiste Joseph 299
Frame, J.S. 504
Francis, J.F.G. 535
Frechet, Maurice, R. 289
Free variables 58 61
Free variables in nonhomogeneous systems 70
frequency 362
Frequency domain 363
Frobenius form 680
Frobenius inequality 221
Frobenius matrix norm 279 425 428
Frobenius matrix norm and inner product 288
Frobenius matrix norm of rank-one matrices 391
Frobenius matrix norm, unitary invariance of 337
Frobenius test for primitivity 678
Frobenius, Ferdinand Georg 44 123 215 662
Full-rank factorization 140 221 633
Full-rank factorization for determining index 640
Full-rank factorization of a projector 393
Function, affine 89
Function, composition of 93 615 608
Function, domain of 89
Function, linear 89 238
Function, norm of 288
Function, range of 89
Functional matrix identities 608
Functions of diagonalizable matrices 526
Functions of Jordan blocks 600
Functions of matrices 601
Functions of matrices, using Cauchy integral formula 611
Functions of matrices, using Cayley — Hamilton theorem 614
Functions of nondiagonalizable matrices 603
Fundamental (normal) mode of vibration 562
Fundamental problem of matrix theory 506
Fundamental subspaces 169
Fundamental subspaces, dimension of 199
Fundamental subspaces, orthonormal bases for 407
Fundamental subspaces, projector onto 434
Fundamental theorem of algebra 185 492
Fundamental theorem of linear algebra 405
Gap 453 454
Gauss — Jordan method 15 47 48
Gauss — Jordan method for computing a matrix inverse 118
Gauss — Jordan method, operation counts 16
Gauss — Markov theorem 229 448
Gauss — Seidel method 622
Gauss, Carl F. ix 2 93 234 488
Gauss, Carl F., as a teacher 353
Gaussian elimination 2 3
| Gaussian elimination and LTJ factorization 141
Gaussian elimination, effects of roundoff 129
Gaussian elimination, modified 43
Gaussian elimination, numerical stability 348
Gaussian elimination, operation counts 10
Gaussian transformation 341
General solution, algebraic equations, homogeneous systems 59 61
General solution, algebraic equations, nonhomogeneous systems 64 66 70 180 221
General solution, difference equations 616
General solution, differential equations 541 609
Generalized condition number 426
Generalized eigenvalue problem 571
Generalized eigenvectors 593 594
Generalized inverse 221 393 422 615
Generalized inverse and orthogonal projectors 434
Generalized inverse, Drazin 399
Generalized inverse, group 402
Generalized minimal residual (GMRES) 655
Genes and chromosomes 543
Geometric multiplicity 510
Geometric series 126 527 618
Gerschgorin circles 498
Gerschgorin, S.A. 497
Givens reduction 344
Givens reduction and determinants 485
Givens reduction, numerical stability 349
Givens rotations 333
Givens, Wallace 333
gmres 655
Golub, Gene H. xii
Gradient 570
Gram matrix 307
Gram — Schmidt algorithm and minimum polynomial 643
Gram — Schmidt algorithm and volume 431
Gram — Schmidt algorithm, classical version 309
Gram — Schmidt algorithm, implementations of 319
Gram — Schmidt algorithm, modified version 316
Gram — Schmidt algorithm, numerical stability of 349
Gram — Schmidt process 345
Gram — Schmidt sequence 308 309
Gram, Jorgen P. 307
Graph 202
Graph of a matrix 209 671
Graphics, 3-D rotations 328 330
Grassmann, Hermann G, 160
Graybill, Franklin A. xii
Grid norm 274
Grid points 18
Group inverse 402 640 641
Group, finite 676
Growth in Gaussian elimination 26
Guttman, L. 124
Hadamard's inequality 469
Hadamard, Jacques 469 497
Halmos, Paul xii 268
Hamilton, William R. 509
Harmonic functions 563
Haynsworth, Emilie V. 123
Heat equation 563
Helfrich, Laura xii
Hermite interpolation polynomial 607
Hermite normal form 48
Hermite polynomial 231
Hermite, Charles 48
Hermitian matrix 85 409 410
Hermitian matrix, condition of eigenvalues 552
Hermitian matrix, eigen components of 549
Hessenberg matrices 350
Hessenberg matrices QR factorization of 352
Hessian matrix 570
Hestenes, Magnus R. 656
Hidden surfaces 332 339
Hilbert matrix 14 31 39
Hilbert — Schmidt norm 279
Hilbert, David 307
Hoelder's inequality 274 277 278
Hoelder, Ludwig O. 278
Hohn, Franz xii
Homogeneous systems 57 61
Hooke's law 86
Hooke, Robert 86
Horn, Roger xii
Horst, Paul 504
Householder reduction 341 342
Householder reduction and determinants 485
Householder reduction and fundamental subspaces 407
Householder reduction, numerical stability 349
Householder transformations 324
Householder, Alston S. 324
Hyperplane 442
Idempotent 113 258 339 386
Idempotent and projectors 387
Identity matrix 106
Identity operator 238
Ill-conditioned matrix 127 128 415
Ill-conditioned system 33 535
Ill-conditioned system, normal equations 214
Image and image space 168 170
Image and image space, dimension of 208
Image of unit sphere 417
Imaginary, pure 556
Imprimitive matrices 674
Imprimitive matrices, maximal root of 676
Imprimitive matrices, spectrum of 677
Imprimitive matrices, test for 678
Imprimitivity, index of 679 680
Incidence matrix 202
Inconsistent system 53
Independent columns 218
Independent eigenvectors 511
Independent rows 218
Independent set 181
Independent set, basic facts 188
Independent set, maximal 186
Independent solutions for algebraic equations 209
Independent solutions for differential equations 481
Index of a square matrix 394 395
Index of a square matrix by full-rank factorization 640
Index of an eigenvalue 401 587 596
Index of imprimitivity 674 679 680
Index of nilpotency 396
Induced matrix norm 280 389
Induced matrix norm of  285
Induced matrix norm of rank-one matrices 391
Induced matrix norm, elementary properties 285
Induced matrix norm, unitary invariance of 337
Inertia 568
Infinite series and matrix functions 527
Infinite series of matrices 605
Infinite-dimensional spaces 195
Information retrieval 419
Inner product 286
Inner product, geometric interpretation 431
Input—output economic model 681
Integer matrices 156 473 485
Integer multiplication 375
Integral formula for generalized inverses 441
Integral formula for matrix functions 611
Intercept model 447
Interchange matrices 135 140
Interlacing of eigenvalues 552
Interpolation, formula for f(A) 529
Interpolation, Hermite polynomial 607
Interpolation, Lagrange polynomial 186
Intersection of subspaces, basis for 211
Intersection of subspaces, projection onto 441
Invariant subspace 259 262 263
Inverse Fourier transform 358
Inverse iteration 534
Inverse matrix 115
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