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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:

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

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Предметный указатель

Inverse matrix of a sum      220
Inverse matrix, best approximation to      428
Inverse matrix, Cauchy formula for      615
Inverse matrix, computation of      118
Inverse matrix, computation of, operation counts      119
Inverse matrix, continuity of      480
Inverse matrix, determinants      479
Inverse matrix, eigenvalues of      501
Inverse matrix, existence of      116
Inverse matrix, generalized      615
Inverse matrix, integral representation of      441
Inverse matrix, norm of      285
Inverse matrix, properties of      120
Invertible operators      246 250
Invertible part of an operator      399
Involutory      113 325 339 485
Irreducible Markov chain, limits      693
Irreducible matrix      209 671
Isometry      321
Iteration matrix      620
Iterative methods      620
Jacobi's diagonalization method      353
Jacobi's iterative method      622 626
Jacobi, Karl G.J.      353
Johnson, Charlie      xii
Jordan blocks      588 590
Jordan blocks, functions of      600
Jordan blocks, nilpotent      579
Jordan chains      210 401 575 576 593
Jordan chains, construction of      594
Jordan form      397 408 589 590
Jordan form for nilpotent matrices      579
Jordan form, preliminary version      397
Jordan segment      588 590
Jordan structure of matrices      580 581 586 589
Jordan structure of matrices, uniqueness of      580
Jordan, Marie Ennemond Camille      15 411 589
Jordan, Wilhelm      15
Kaczmarz's projection method      442 443
Kaczmarz, Stefan      442
Kaplansky, Irving      268
Kearn, Vickie      xi 12
Kernel      173
Kirchhoff's rules      73
Kirchhoff's rules, loop rule      204
Kline, Morris      80
Kowa, Seki      459
Kronecker product      380 597
Kronecker product and the Laplacian      573
Kronecker, Leopold      597
Krylov, Aleksei Nikolaevich      645
Krylov, method      649
Krylov, sequence      401
Krylov, subspaces, sequences, matrices      646
Kummer, Ernst Eduard      597
Lagrange interpolating polynomial      186 230 233
Lagrange multipliers      282
Lagrange, Joseph-Louis      186 572
Lancaster, Peter      xii
Lanczos algorithm      651
Lanczos, Cornelius      651
Laplace's determinant expansion      487
Laplace's equation      624
Laplace, Pierre-Simon      81 307 487 572
Laplacian      563
Latent semantic indexing      419
Latent values and vectors      490
Law of Cosines      295
LDU factorization      154
Leading principal minor      558
Leading principal submatrices      148 156
Least common multiple      647
Least squares      226 439
Least squares and Gram — Schmidt      313
Least squares and orthogonal projection      437
Least squares and polynomial fitting      230
Least squares and pseudoinverse      438
Least squares and QR factorization      346
Least squares, total least squares      223
Least squares, why least squares?      446
LeBlanc, Kathleen      xii
Left-hand eigenvectors      490 503 516 523 524
Left-hand eigenvectors and projectors      518
Left-hand eigenvectors in inverses      521
Left-hand nullspace      174 178 199
Left-hand nullspace, spanning set for      176
Legendre polynomials      319
Legendre's differential equation      319
Legendre, Adrien-Marie      319 572
Leibniz, Gottfried W.      459
Length of a projection      323
Leontief's input—output model      681
Leontief, Wassily      681
Leslie population model      683
Leslie, P.H.      684
Leverrier — Souriau — Frame Algorithm      504
Leverrier, U.J.J.      504
Levy, L.      497
Limiting distribution      531 636
Limits and group inversion      640
Limits and spectral radius      617
Limits in Markov chains, irreducible Markov chains      693
Limits in Markov chains, reducible Markov chains      698
Limits in vector spaces      276 277
Limits of powers of matrices      630
Limits of vector sequences      639
Lindemann, Carl Louis Ferdinand von      662
Linear algebra      238
linear combination      91
Linear correlation      296 306
Linear dependence and connectivity      208
Linear estimation      446
Linear functions      89 238
Linear functions, defined by matrix multiplication      106
Linear functions, defined by systems of equations      99
Linear models      448
Linear operators      238
Linear operators and block matrices      392
Linear regression      227 446
Linear spaces      169
Linear stationary iterations      620
Linear transformation      238
Linearly independent and dependent sets      181
Linearly independent and dependent sets, and rank      183
Linearly independent and dependent sets, basic facts      188
Linearly independent and dependent sets, maximal      186
Linearly independent eigenvectors      511
Lines in $\mathfrak{R}^{n}$ not through the origin      440
Lines, projection onto      440
Long-run distribution      531
Loop      73
Loop, equations      204
Loop, rule      74
Loop, simple      75
Lower triangular      103
LU factorization      141 144
LU factorization with interchanges      148
LU factorization, existence of      149
LU factorization, operation counts      146
LU factorization, summary      153
M-matrix      626 639 682 703
Main diagonal      41 85
Markov chains      532 638 687
Markov chains, absorbing      700
Markov chains, periodic      694
Markov, Andrei Andreyevich      687
Mass-stiffness equation      571
Matrices, the set of      81
Matrix      7
Matrix, diagonal      85

Matrix, exponential      441 525 529
Matrix, exponential, and differential equations      541 546 608
Matrix, exponential, inverse of      614
Matrix, exponential, products      539
Matrix, exponential, sums      614
Matrix, functions      526 601
Matrix, functions, as infinite series      527
Matrix, functions, as polynomials      606
Matrix, group      402
Matrix, multiplication      96
Matrix, multiplication as a linear function      106
Matrix, multiplication by blocks      111
Matrix, multiplication, properties of      105
Matrix, multiplication, relation to linear transformations      244
Matrix, norms      280
Matrix, norms, $\infty$ -norm      127 283
Matrix, norms, 1-norm      283
Matrix, norms, 2-norm      281 425
Matrix, norms, Frobenius norm      425
Matrix, norms, induced norm      285
Matrix, polynomials      501
Matrix, product      96
Matrix, representation of a projector      387
Matrix, representations      262
Matrix, triangular      41
Maximal angle      455
Maximal independent set      218
Maximal linearly independent subset      186 196
Maximum and minimum of continuous functions      276
McCarthy, Joseph R.      651
Mean      296 447
Meyer, Bethany B.      xii
Meyer, Carl, Sr.      xii
Meyer, Holly F.      xii
Meyer, Louise      xii
Meyer, Margaret E.      xii
Meyer, Martin D.      xii
Min-max theorem      550
Min-max theorem for singular values      555
Min-max theorem, alternate formulation      557
Minimal angle      450
Minimal spanning set      196 197
Minimum norm least squares solution      438
Minimum norm solution      426
Minimum polynomial      642
Minimum polynomial of a vector      646
Minimum polynomial, determination of      643
Minimum variance estimator      446
Minkowski inequality      278
Minkowski, Hermann      184 278 497 626
Minor determinant, principal      559 466
MINRES algorithm      656
Mirsky, Leonid      xii
Modern least squares      437
Modified gaussian elimination      43
Modified Gram — Schmidt algorithm      316
Monic polynomial      642
Montgomery, Michelle      xii
Moore — Penrose generalized inverse      221 422 400
Moore — Penrose generalized inverse and orthogonal projectors      434
Moore — Penrose generalized inverse, best approximate inverse      428
Moore — Penrose generalized inverse, integral representation      441
Moore, E.H.      221
Morrison, W.J.      124
Multiplication of integers      375
Multiplication of matrices      96
Multiplication of polynomials      367
Multiplicities      510
Multiplicities and diagonalizability      512
Multiplier      22 25
Multiplier in partial pivoting      26
Negative definite      570
Neumann series      126 527 618
Newton      86
Newton's identities      504
Newton's second law      560
Nilpotent      258 396 502 510
Nilpotent, Jordan blocks      579
Nilpotent, part of an operator      399
No-intercept model      447
Noble, Ben      xii
Node      18 73 202 204
Node, rule      74 204
Noise removal with SVD      418
Nonbasic columns      50 61
Nonderogatory matrices      644 648
Nondiagonalizable, spectral resolution      603
Nonhomogeneous differential equations      609
Nonhomogeneous systems      57 64
Nonhomogeneous systems, general solution      64 66 70
Nonhomogeneous systems, summary      70
Nonnegative matrices      661 670
Nonsingular matrices      115
Nonsingular matrices and determinants      465
Nonsingular matrices and elementary matrices      133
Nonsingular matrices, products of      121
Nonsingular matrices, sequences of      220
Norm      269
Norm for matrices      280
Norm for matrices, 1-, 2-, and $\infty$ -norms      281 283
Norm for matrices, Frobenius      279 337
Norm for matrices, induced      280 285 337
Norm for vectors      275
Norm for vectors, 1-, 2-, and $\infty$ -norms      274
Norm for vectors, p-norms      274
Norm of a function      288
Norm of a projection      323 391
Norm of a waveform      382
Norm of an inverse      285
Norm on a grid      274
Norm, compatibility      279 280 285
Norm, elliptical      288
Norm, equivalent      276 425
Normal equations      213 214 221 226 313 437
Normal matrix      304 400 409 547
Normal modes of vibration      562 571
Normalized vector      270
Nullity      200 220
NullSpace      173 174 178 199
Nullspace and transpose      177
Nullspace of a partitioned matrix      208
Nullspace of a product      180 220
Nullspace of an orthogonal projector      434
Nullspace, equality      177
Nullspace, spanning set for      175
Number of pivots      218
Numerical stability      347
Oblique projection      385
Oblique projection, method for linear systems      443
Oblique projectors from SVD      634
Oh notation $O(h^{p})$       18
Ohm's law      73
One-to-one mapping      250
Onto mapping      250
Operation counts for convolution      377
Operation counts for Gauss — Jordan method      16
Operation counts for Gaussian elimination      10
Operation counts for LU factorization      146
Operation counts for matrix inversion      119
Operator norm      280
Operator, linear      238
Ortega, James      xii
Orthogonal complement      322 403
Orthogonal complement, dimension of      339
Orthogonal complement, involving range and nullspace      405
Orthogonal decomposition theorem      405 407
Orthogonal diagonalization      549
Orthogonal distance      435
Orthogonal matrix      320
Orthogonal matrix, determinant of      473

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