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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 |
SIAM 324 333
Sign of a permutation 461
Signal processing 359
Signal-to-noise ratio 418
Similar matrices 255 473 506
Similarity 505
Similarity and block-diagonal matrices 263
Similarity and block-triangular matrices 263
Similarity and eigenvalues 508
Similarity and orthogonal matrices 549
Similarity and transpose 596
Similarity, invariant 256
Similarity, transformation 255 408 506
Similarity, unitary 547
Simple eigenvalue 510
simple loops 75
Simultaneous diagonalization, triangularization 522
Simultaneous displacements 622
Sine, discrete 361
Singular matrix 115
Singular matrix, eigenvalues of 501
Singular matrix, sequences of 220
Singular systems, practical solution of 217
Singular values 553
Singular values and determinants 473
Singular values and the SVD 412
Singular values as eigenvalues 555
Singular values, Courant — Fischer theorem 555
SIZE 8
Skew-Hermitian matrices 85 88
Skew-symmetric matrices 85 88 391 473
Skew-symmetric matrices as exponentials 539
Skew-symmetric matrices, eigenvalues of 549 556
Skew-symmetric matrices, vector space of 436
SOR method 624
Souriau, J.M. 504
Spanning sets 165
Spanning sets for column space 172
Spanning sets for four fundamental subspaces 178
Spanning sets for left-hand nullspace 176
Spanning sets for nullspace 175
Spanning sets for row space 172
Spanning sets, minimal 197
Spanning sets, test for 172
Sparse least squares 237
Sparse matrix 350
Spectral circle, imprimitive matrices 676
Spectral mapping property 539 613
Spectral projectors 517 602 603
Spectral projectors in terms of eigenvectors 518
Spectral projectors, commuting property 522
Spectral projectors, interpolation formula for 529
Spectral projectors, positivity of 677
Spectral radius 497 521 540
Spectral radius and limits 617
Spectral radius as a limit 619
Spectral radius, Collatz — Wielandt formula 666 673 686
Spectral representation of matrix functions 526
Spectral resolution of f(A) 603
Spectral theorem for diagonalizable matrices 517
Spectrum 490
Spectrum of imprimitive matrix 677
Spheres 275
Splitting 620
Spring-mass vibrations 570
springs 86
Square, matrix 8
Square, system 5
Square, wave function 301
Stable 544
Stable, algorithm 217 317 347 422
Stable, matrix 544
Stable, system 544 609
Standard basis 194 240 299
Standard coordinates 240
Standard deviation 296
Standard inner product 95 271
Standard scores 296
Standardization of data 296
Stationary distribution 531 693
Steady-state distribution 531 636
Steepest descent 657
Step size 19
Stewart, G.W. xii
Stiefel, Eduard 656
Stiffness, constant 86
Stiffness, matrix 87
Stochastic matrix 685 687
Stochastic matrix, doubly 702
Stochastic matrix, summability of 697
Stochastic matrix, unit eigenvalues of 696
Strang, Gilbert xii
Strongly connected graph 209 671
Strutt, John W. 550
Stuff in a vector space 197 200
Subgroup 402
SubMatrix 7
Submatrix and rank 215
Submatrix as a block matrix 111
Subscripts 7
Subset 162
subspace 162
Subspace, angles or gaps between 450
Subspace, dimension of 198
Subspace, directed distance between 453
Subspace, four fundamental 169
Subspace, invariant 259 262 263
Subspace, maximal angle between 455
Subspace, sum of 205
Substochastic matrix 685
Successive displacements 623
Successive over relaxation method 624
Sum of matrices 81
Sum of orthogonal projectors 441
Sum of projectors 393
Sum of vector spaces 166 383
Sum of vector spaces, dimension of 205
Summable matrix and summability 631 633 677
Summable matrix and summability, stochastic matrices 697
Superdiagonal 575
SVD 412
SVD and full-rank factorization 634
| SVD and oblique projectors 634
Switching circuits 539
Sylvester's law of inertia 568
Sylvester's law of nullity 220
Sylvester, James J. 44 80 411
Symmetric functions 494
Symmetric matrices 85
Symmetric matrices, diagonalization and eigen components of 549
Symmetric matrices, reduction to tridiagonal form 352
Symmetric matrices, space of 436
Symmetric permutation 671
t-digit arithmetic 21
Taussky-Todd, Olga 497
Taylor series 18 570 600
Tensor product 380 597
Tensor product and the Laplacian 573
Term-by-document matrix 419
Text mining 419
Three-dimensional rotations 328 330
Time domain 363
Todd, John 497
Toeplitz matrices 514
Toeplitz, Otto 514
Total least squares 223
Trace 90
Trace and characteristic equation 504
Trace as sum of eigenvalues 494
Trace of a linear operator 256
Trace of a product 110 114
Trace of a projector 392
Trace of imprimitive matrices 678
Trace, inequalities 293
Transformation, linear 238
Transient behavior 532
Transient class 695
Transition diagram 108 531
Transition matrix 108 531 688
Transitive operations 257
Translation, in 3-D graphics 332
TRANSPOSE 83
Transpose and determinants 463
Transpose and similarity 596
Transpose, nullspace 177
Transpose, properties of 84
Transpose, reverse order law for 109
Trapezoidal form 342
Trend of observations 231
Triangle inequality 220 273 277
Triangle inequality, backward version 273
Triangular matrices 41 103
Triangular matrices, block versions 112
Triangular matrices, determinant of 462
Triangular matrices, eigenvalues of 501
Triangular matrices, elementary 142
Triangular matrices, inverses of 122
Triangular system 6
Triangularization using elementary reflectors 342
Triangularization, simultaneous 522
Tridiagonal matrix 20 156 352
Tridiagonal matrix, Toeplitz matrices 514
Trivial nullspaces 175
Trivial solution 57 60 69
Trivial solution and nonhomogeneous systems 70
Trivial solution and nonsingular matrices 116
Trivial subspace 162 197
Tukey, J.W. 368 375 651
Two-point boundary value problem 18
Unbiased estimator for variance 449 446
Uncertainties in linear systems 414
Underrelaxation 624
Unique solution and free variables 61
Unique solution for differential equations 541
Unique solution for homogeneous systems 61
Unique solution for nonhomogeneous systems 70
Unit columns 102 107
Unit eigenvalues of stochastic matrices 696
Unit sphere 275
Unit sphere, image of 414 425
Unitarily invariant norm 425 337
Unitary diagonalization 547
Unitary matrices 304 320
Unitary matrices, determinant of 473
UNITS 27
Unstable 544
Upper triangular 103
Upper-trapezoidal form 342 344
URV factorization 406 407
URV factorization and full-rank factorization 634
Van Loan, Charlie xii
Vandermonde determinant 486
Vandermonde matrices 185 230 357
Vandermonde, Alexandre-Theophile 185
Variance 447
Vector 159
Vector, norms 274
Vector, spaces 160
Vertex matrix 330
Vibrations, small 559
Volume by determinants 468
Volume by Gram — Schmidt, and QR 431
von Mises, R. 533
von Neumann, John 289
Weierstrass, Karl Theodor Wilhelm 589 662
Well conditioned 33 127 415
Weyl, Hermann 160
Why least squares? 446
Wielandt's matrix 685
Wielandt's theorem 675
Wielandt, Helmut 534 666 675 679
Will, Marianne xii
Wire frame figure 330
Woodbury, M. 124
Wronski matrix 189 190
Wronski, Jozef M. 189
wronskian 474 481 486
Young, David M. 625
Young, G. 411
Z-matrix 628 639 296
z-scores 296
Zeeman, E. Christopher 704
Zero nullspace 175
Zero transformation 238
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