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Meyer C.D. — Matrix analysis and applied linear algebra
Meyer C.D. — Matrix analysis and applied linear algebra



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Название: Matrix analysis and applied linear algebra

Автор: Meyer C.D.

Аннотация:

In this text, Meyer (mathematics, North Carolina State U.) circumvents the traditional definition-theorem-proof format by focusing on applications. He includes some of the more contemporary topics of applied linear algebra, uses modern concepts and notation, and accompanies theoretical developments with examples. The eight chapters cover linear equations, rectangular systems and echelon forms, matrix algebra, vector spaces, determinants, Eigenvalues and Eigenvectors, Perron-Frobenius theory, and norms, inner products, and orthogonality. The included CD-ROM contains a searchable copy of the entire textbook and all solutions, as well as detailed information on topics mentioned in examples, references, thumbnail sketches and photographs of mathematicians, and a history of linear algebra and computing.


Язык: en

Рубрика: Математика/Алгебра/Линейная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 718

Добавлена в каталог: 21.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Orthogonal projection and 3-D graphics      330
Orthogonal projection and least squares      437
Orthogonal projection, onto an affine space      436
Orthogonal projectors      322 410 427 429
Orthogonal projectors and pseudoinverses      434
Orthogonal projectors, elementary      431
Orthogonal projectors, formulas for      430
Orthogonal projectors, onto an intersection      441
Orthogonal projectors, sums of      441
Orthogonal reduction      341
Orthogonal reduction to determine full-rank factorization      633
Orthogonal reduction to determine fundamental subspaces      407
Orthogonal triangularization      342
Orthogonal vectors      294
Orthonormal basis      98
Orthonormal basis by means of orthogonal reduction      355
Orthonormal basis for fundamental subspaces      307
Orthonormal basis, extending to      25 335 38
Orthonormal set      298
Ostrowski, Alexander      626
Outer product      103
Overrelaxation      624
p-Norm      274
Painter, Richard J.      xii
Parallel sum      441
Parallelepiped      431 468
Parallelogram identity      290 291
Parallelogram law      162
Parity of a permutation      460
Parseval des Chenes, M.      305
Parseval's identity      305
Partial pivoting      24
Partial pivoting and diagonal dominance      193
Partial pivoting and LU factorization      148
Partial pivoting and numerical stability      349
Particular solution      58 65—68 70 180 213
Partitioned matrix      111
Partitioned matrix and linear operators      392
Partitioned matrix, rank and nullity of      208
Peano, Giuseppe      160
Penrose equations      422
Penrose, Roger      221
Perfect shuffle      372 381
Period of trigonometric functions      362
periodic extension      302
Periodic function      301
Periodic Markov chain      694
Permutation      460
Permutation counter      151
Permutation matrix      135 140 151
Permutation, symmetric      671
Perp, properties of      404 409
Perpendicular      294
Perron root      666 668
Perron vector      665 668 673
Perron — Frobenius theory      661 673
Perron, Oskar      661
Perturbations in inverses      128
Perturbations in linear systems      33 128 217
Perturbations, affecting rank      216
Perturbations, eigenvalues      528
Perturbations, eigenvalues, hermitian eigenvalues      551
Perturbations, rank-one update      208
Perturbations, singular values      421
Piazzi, Giuseppe      233
Pivot conditioning      426
Pivot determinant formula for      474 558
Pivot elements and equations      5
Pivot positions      5 58 61
Pivot positions in partial pivoting      24
Pivot uniqueness      44
Pivoting, complete      28
Pivoting, partial      24
Plane rotation      333
Plane rotation, determinant of      485
Poisson's equation      563 572
Poisson, Simeon D.      78 572
Polar factorization      572
Polarization identity      293
Polynomial and matrix functions      606
Polynomial equations      493
Polynomial in a matrix      501
Polynomial, minimum      642
Polynomial, multiplication and convolution      367
Polytope      330 339
Ponderal index      236
Poor man's root finder      649
Population distribution      532
Population migration      531
Population model, Leslie      683
Positive definite form      567
Positive definite matrix      154 474 558 559
Positive matrix      661 663
Positive semidefinite matrix      558 566
Poulson, Deborah      xii
Power method      532 533
Powers of a matrix      107
Powers of a matrix, limiting values      530
Powers of linear transformations      248
PRECISION      21
Preconditioned system      658
Predator-prey model      544
Primitive matrices      674
Primitive matrices, test for      678
Principal angles      456
Principal minors      494 558
Principal minors in an M-matrix      626 639
Principal minors, nonnegative      566
Principal minors, positive      559
Principal submatrix      494 558
Principal submatrix and interlaced eigenvalues      553
Principal submatrix of a stochastic      703
Principal submatrix of an M-matrix      626
Product rule for determinants      467
Products of matrices      96
Products of nonsingular matrices      121
Products of orthogonal projectors      441
Products of projectors      393
Projection      92 94 322 385 429
Projection and Fourier expansion      440
Projection, method for solving linear systems      442 443
Projection, onto, affine spaces      436
Projection, onto, fundamental subspaces      434
Projection, onto, hyperplanes      442
Projection, onto, lines      440 431
Projection, onto, oblique subspaces      385
Projection, onto, orthogonal subspaces      429
Projection, onto, symmetric matrices      436
projectors      239 243 339 385 386
Projectors as idempotents      387
Projectors from core-nilpotent decomposition      398
Projectors from full-rank factorization      633 634
Projectors, complementary      386
Projectors, difference of      393
Projectors, induced norm of      389
Projectors, matrix representation of      387
Projectors, oblique      386
Projectors, orthogonal      429
Projectors, product of      393
Projectors, spectral      517 603
Projectors, sum of      393
Proper values and vectors      490
Pseudoinverse      221 422 615
Pseudoinverse and least squares      438
Pseudoinverse and orthogonal projectors      434
Pseudoinverse as best approximate inverse      428
Pseudoinverse group      402
Pseudoinverse, Drazin      399
Pseudoinverse, inner, outer, reflexive      393
Pseudoinverse, integral representation of      441 615
Pseudoinverse, Moore — Penrose      422
Pure imaginary      556
Pythagorean Theorem      294 305 423
Pythagorean theorem and closest point theorem      435
Pythagorean theorem for matrices with Frobenius norm      428
QR factorization      345 535
QR factorization and Hessenberg matrices      352
QR factorization and least squares      346
QR factorization and minimum polynomial      643
QR factorization and volume      431
QR factorization, rectangular version of      311
Quadratic form      567
Quaternions      509
Random integer matrices      156
Random walk      638
Range of a function      89 169
Range of a matrix      170 171 178 199
Range of a partitioned matrix      179
Range of a product      180 220
Range of a projector      391
Range of a sum      206
Range of an operator      250
Range of an orthogonal projector      434
Range-nullspace decomposition      394 407
Range-symmetric matrices      408
Rank      45 139
Rank and consistency      54
Rank and determinants      466
Rank and free variables      61
Rank and independent sets      183
Rank and matrix inverses      116
Rank and nonhomogeneous systems      70
Rank and nonsingular submatrices      218
Rank and submatrices      215
Rank and trivial nullspaces      175
Rank normal form      136
Rank of a block diagonal matrix      137
Rank of a difference      208
Rank of a partitioned matrix      208
Rank of a perturbed matrix      216
Rank of a product      210 211 219
Rank of a projector      392
Rank of a sum      206 221
Rank of an elementary projector      337
Rank of an incidence matrix      203
Rank plus nullity theorem      199 410
Rank summary      218
Rank, numerical determination      421
Rank-one matrices, characterization of      140
Rank-one matrices, diagonalizability of      522
Rank-one matrices, perturbations of      208
Rank-one updates, determinants of      475
Rank-one updates, eigenvalues of      503
Rayleigh quotient      550
Rayleigh quotient, iteration      535
Rayleigh, Lord      550
Real numbers, the set of      81
Real Schur form      524
Real-symmetric matrix      409 410
Rectangular matrix      8
Rectangular QR factorization      311
Rectangular systems      41
Reduced row echelon form      48
Reducible Markov chain      698
Reducible matrices      209 671
Reducible matrices in linear systems      112
Reducible matrices, canonical form for      695
Reflection      92 94
Reflection about a hyperplane      445
Reflection, method for solving linear systems      445
Reflector      239 324 444
Reflector, determinant of      485
Reflexive pseudoinverse      393
Regression      227 446
Relative uncertainty or error      414
Relaxation parameter      445 624
Residual      36 416
Resolvent      285 611
Restricted operators      259 393 399
Restricted transformations      424
Reversal matrix      596
Reverse order law for inversion      120 121
Reverse order law for transpose and conjugate transpose      109
Reversing binary bits      372
Richardson iterative method      622
Right angle      294
Right-hand rule      340
Right-hand side      3
Ritz values      651
Roots of unity      356
Roots of unity and imprimitive matrices      676
Rose, Nick      xii
Rotation      92 94
Rotation plane (Givens rotations)      333
Rotation, determinant of      485
Rotation, in \mathfrak{R}^2$      326
Rotation, in \mathfrak{R}^3$      328
Rotation, in \mathfrak{R}^n$      334
Rotator      239 326
Rounding convention      21
Roundoff error      21 129 347
Row      7
Row and nullspace      177
Row equivalence      134 218
Row operations      134
Row rank      198
Row relationships      136
Row space      170 171 178 199
Row vector      8 81
Row, echelon form      44
Row, reduced      48
Row, scaling      27
Row, spanning set for      172
RPN matrices      408
Rutishauser, Heinz      535
Saad, Yousef      655
Saw-toothed function      306
scalar      7 81
Scalar multiplication      82 83
SCALE      27
Scaling a linear system      27 28
Scaling in 3-D graphics      332
Schmidt, Erhard      307
Schroedinger, Erwin      651
Schultz, Martin H.      655
Schur complements      123 475
Schur form for real matrices      524
Schur norm      279
Schur triangularization theorem      508
Schur, Issai      123 508 662
Schwarz, Hermann A.      271 307
Search engine      418 419
Sectionally continuous      301
Secular equation      503
Seidel, Ludwig      622
Sellers, Lois      xii
Semiaxes      414
Semidefinite      566
Semisimple eigenvalue      510 591 593 596
Semistable      544
Sensitivity      128
Sensitivity, minimum norm solution      426
Sequence of matrices      220
Sequence, limit of      639
Series for f(A)      605
SHAPE      8
Shell game      635
Sherman — Morrison formula      124 130
Sherman, J.      124
SIAM      324 333
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