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Carl D. Meyer — Matrix Analysis and Applied Linear Algebra Book and Solutions Manual
Carl D. Meyer — Matrix Analysis and Applied Linear Algebra Book and Solutions Manual



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Название: Matrix Analysis and Applied Linear Algebra Book and Solutions Manual

Автор: Carl D. Meyer

Аннотация:

Although titled as Matrix Analysis and Applied Linear Algebra, this book is one of the clearest treatments of pure linear algebra in general. Most of the theorems are proved and the proofs are very well motivated. There are no hand-waving arguments yet it is very easy to follow all the material contained. I also noticed that this book provides a smooth transition to introductory functional analysis for those who already possess the adequate real analysis background.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 700

Добавлена в каталог: 26.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $A^{-1}$      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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