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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
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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