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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
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 transformation      255 408 506
Similarity, invariant      256
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 — Ponderal index      236
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 matrices      697
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 overrelaxation 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
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 inequalities      293
Trace of a linear operator      256
Trace of a product      110 114
Trace of a projector      392
Trace of imprimitive matrices      678
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
1 2 3 4 5
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