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| Carl D. Meyer — Matrix Analysis and Applied Linear Algebra Book and Solutions Manual |
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| Предметный указатель |
Absolute uncertainty or error 414
Absorbing Markov chains 700
Absorbing states 700
Addition, properties of 82
Additive identity 82
Additive inverse 82
Adjacency matrix 100
Adjoint 84 479
Adjugate 479
Affine functions 89
Affine space 436
Algebraic group 402
Algebraic multiplicity 496 510
Amplitude 362
Anderson — Duffin formula 441
Anderson, Jean xii
Anderson, W.N., Jr. 441
angle 295
Angle between complementary spaces 389 450
Angle between subspaces 450
Angle, canonical 455
Angle, maximal 455
Angle, principal 456
Annihilating polynomials 642
Aperiodic Markov chain 694
Arnoldi's algorithm 653
Arnoldi, Walter Edwin 653
Associative property of addition 82
Associative property of matrix multiplication 105
Associative property of scalar multiplication 83
Asymptotic rate of convergence 621
Augmented matrix 7
Autonne, L. 411
Back substitution 6 9
Backward error analysis 26
Backward triangle inequality 273
Band matrix 157
Bartlett, M.S. 124
Base-b 375
Basic columns 45 61 178 218
Basic columns, combinations of 54
Basic variables 58 61
Basic variables in nonhomogeneous systems 70
Basis 194 196
Basis for direct sum 383
Basis for intersection of spaces 211
Basis for space of linear transformations 241
Basis, change of 253
Basis, characterizations 195
Basis, orthonormal 355
Bauer — Fike bound 528
Beads on a string 559
Bellman, Richard xii
Beltrami, Eugenio 411
Benzi, Michele xii
Bernoulli, Daniel 299
Bessel's inequality 305
Bessel, Friedrich W. 305
Best approximate inverse 428
Biased estimator 446
Binary representation 372
Birkhoff's theorem 702
Birkhoff, Garrett 625
Bit reversal 372
Bit reversing permutation matrix 381
Block diagonal 261-263
Block diagonal, rank of 137
Block diagonal, using real arithmetic 524
Block matrices 111
Block matrices, determinant of 475
Block matrices, linear operators 392
Block matrix multiplication 111
Block triangular 112 261—263
Block triangular, determinants 467
Block triangular, eigenvalues of 501
Bolzano — Weierstrass theorem 670
Boolean matrix 679
Bordered matrix 485
Bordered matrix, eigenvalues of 552
Branch 73 204
Brauer, Alfred 497
Bunyakovskii, Victor 271
Cancellation law 97
Canonical angles 455
Canonical form, reducible matrix 695
Cantor, Georg 597
Cauchy — Bunyakovskii — Schwarz inequality 272
Cauchy — Goursat theorem 615
Cauchy — Schwarz inequality 287
Cauchy, Augustin-Louis 271
Cauchy, Augustin-Louis, determinant formula 484
Cauchy, Augustin-Louis, integral formula 611
Cayley transformation 336 556
Cayley — Hamilton theorem 509 532 597
Cayley — Hamilton theorem to determine f(A) 614
Cayley, Arthur 80 93 158 460
CBS inequality 272 277 473
CBS inequality, general form 287
Centered difference approximations 19
Cesaro sequence 630
Cesaro summability 630 633 677
Cesaro summability for stochastic matrix 697
Cesaro, Ernesto 630
Chain, Jordan 575
Change of basis 251 253 258
Change of coordinates 252
Characteristic equation 491 492
Characteristic equation, coefficients 494 504
Characteristic polynomial 491 492
Characteristic polynomial of a product 503
Characteristic values and vectors 490
Chebyshev, Pafnuty Lvovich 40 687
Checking an answer 35 416
Cholesky factorization 154 314 558 559
Cholesky, Andre-Louis 154
Cimmino's reflection method 445
Cimmino, Gianfranco 445
Circuit 204
Circulant matrix 379
Circulant matrix with convolution 380
Circulant matrix, eigenvalues, eigenvectors 523
Classical Gram — Schmidt algorithm 309
Classical least squares 226
Clock cycles 539 694
Closest point to an affine space 436
Closest point with Fourier expansion 440
Closest point, theorem 435
Closure property of addition 82 160
Closure property of multiplication 83 160
Coefficient matrix 7 42
Coefficient of linear correlation 297
Cofactor 477 487
Cofactor, expansion 478 481
Collatz — Wielandt formula 666 673 686
Collatz, Lothar 666
column 7
Column, equivalence 134
Column, equivalence, and nullspace 177
Column, operations 14 134
Column, rank 198
Column, relationships 50 136
Column, scaling 27
Column, space 170 171 178
Column, space, spanning set for 172
Column, vector 8 81
Comdico, David xii
Commutative law 97
Commutative property of addition 82
Commuting matrices, eigenvectors 503 522
Companion matrix 648
| Compatibility of norms 285
Compatible norms 279 280
Competing species model 546
Complementary projector 386
Complementary subspaces 383 403
Complementary subspaces, angle between 389 450
Complete pivoting 28
Complete pivoting, numerical stability 349
Complete set of eigenvectors 507
Complex conjugate 83
Complex exponential 362 544
Complex numbers, the set of 81
Component matrices 604
Component vectors 384
Composition of linear functions 93
Composition of linear transformations 245 246
Composition of matrix functions 608 615
Computer graphics 328 330
Condition number for eigenvalues 528
Condition number for matrices 127 128 414 415
Condition number, generalized 426
Condition of eigenvalues, hermitian matrices 552
Condition of linear system 128
Conditioning and pivots 426
Conformable 96
Conformably partitioned 111
Congruence transformation 568
Conjugate gradient algorithm 657
Conjugate matrix 84
Conjugate transpose 84
Conjugate transpose, reverse order law 109
Conjugate vectors 657
Conjugate, complex 83
Connected graph 202
Connectivity and linear dependence 208
Connectivity matrix 100
Consistent system 53 54
Constituent matrices 604
Continuity of eigenvalues 497
Continuity of inversion 480
Continuity of norms 277
Continuous Fourier transform 357
Continuous functions, max and min 276
Convergence 276 277
Convergent matrix 631
Converse of a statement 54
Convolution with circulants 380
Convolution, definition 366
Convolution, operation count 377
Convolution, theorem 367 368 377
Cooley, J.W. 368 375 651
Cooperating species model 546
Coordinate matrix 242
Coordinate spaces 161
coordinates 207 240 299
Coordinates of a vector 240
Coordinates, change of 252
Core-nilpotent decomposition 397
Correlation 296
Correlation coefficient 297
Cosine of angle 295
Cosine of angle, minimal angle 450
Cosine, discrete 361
Courant — Fischer theorem 550
Courant — Fischer theorem for singular values 555
Courant — Fischer theorem, alternate 557
Courant, Richard 550
Covariance 447
Cramer's rule 459 476
Cramer, Gabriel 476
Critical point 570
Cross product 332 339
Cuomo, Kelly xii
Curve fitting 186 229
Defective 507
Deficient 496 507
Definite matrices 559
Deflation, eigenvalue problems 516
Dense matrix 350
Dependent set 181
Derivative of a determinant 471 474 486
Derivative of a linear system 130
Derivative of a matrix 103 226
Derivative, operator 245
Determinant 461
Determinant and volume 468
Determinant as product of eigenvalues 494
Determinant of a product 467
Determinant of a sum 485
Determinant, computing 470
Deviation from symmetry 436
Diagonal dominance 639
Diagonal matrix 85
Diagonal matrix, eigenvalues of 501
Diagonal matrix, inverse of 122
Diagonalizability 507
Diagonalizability in terms of minimum polynomial 645
Diagonalizability in terms of multiplicities 512
Diagonalizability, being arbitrarily close to 533
Diagonalizability, summary 520
Diagonalization of circulants 379
Diagonalization of normal matrices 547
Diagonalization, Jacobi's method 353
Diagonalization, simultaneous 522
Diagonally dominant 184 499 622 623 639
Diagonally dominant, systems 193
Difference equations 515 616
Difference of matrices 82
Difference of projectors 393
Differential equations 489 541 542
Differential equations, independent solutions 481
Differential equations, nonhomogeneous 609
Differential equations, solution of 546
Differential equations, stability 544 609
Differential equations, systems 608
Differential equations, uncoupling 559
Diffusion equation 563
Diffusion model 542
DIMENSION 196
Dimension of direct sum 383
Dimension of fundamental subspaces 199
Dimension of left-hand nullspace 218
Dimension of nullspace 218
Dimension of orthogonal complement 339
Dimension of range 218
Dimension of row space 218
Dimension of space of linear transformations 241
Dimension of subspace 198
Dimension of sum 205
Direct product 380 597
Direct sum 383
Direct sum of linear operators 399
Direct sum of several subspaces 392
Direct sum of symmetric and skew-symmetric matrices 391
Directed distance between subspaces 453
Directed graph 202
Dirichlet problem 563
Dirichlet, Johann P.G.L. 563 597
Discrete Fourier Transform 356 358
Discrete Laplacian 563
Discrete Laplacian, eigenvalues of 598
Discrete sine, cosine, and exponential 361
Disjoint subspaces 383
Distance 271
Distance between a vector and a subspace 435
Distance between subspaces 450
Distance to lower-rank matrices 417
Distance to symmetric matrices 436
Distinct eigenvalues 514
Distributions 532
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