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| Авторизация |
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| Поиск по указателям |
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| Lay D.C. — Linear Algebra And Its Applications |
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| Предметный указатель |
Matrix (matrices), lower triangular 127 128
Matrix (matrices), migration 88 260 286
Matrix (matrices), multiplication of 99 122
Matrix (matrices), null space, of 200
Matrix (matrices), orthogonal 346 405
Matrix (matrices), orthogonal projection see “Projection matrix”
Matrix (matrices), orthogonally diagonalizable 406
Matrix (matrices), orthonormal 346
Matrix (matrices), partitioned 121
Matrix (matrices), Pauli spin 158
Matrix (matrices), positive definite 417
Matrix (matrices), positive semidefinite 417
Matrix (matrices), product of 99
Matrix (matrices), rank of 238
Matrix (matrices), reduced echelon 13
Matrix (matrices), regular stochastic matrix 264
Matrix (matrices), right-multiplication 176
Matrix (matrices), row reduced 14
Matrix (matrices), row space of 235
Matrix (matrices), scalar multiple of 97 122
Matrix (matrices), similar 284
Matrix (matrices), singular values of 428
Matrix (matrices), size of 5
Matrix (matrices), standard 80
Matrix (matrices), stiffness 109
Matrix (matrices), stochastic 259 268 273 320
Matrix (matrices), strictly diagonally dominant 141
Matrix (matrices), submatrix of 270
Matrix (matrices), sum of 97 122
Matrix (matrices), symmetric 328 405 417 421
Matrix (matrices), trace of 303 438
Matrix (matrices), transpose of 104
Matrix (matrices), triangular 13 165
Matrix (matrices), Vandermonde 158 187 330
Matrix equation(s) 38 49 54
Matrix factorization(s) 128
Matrix factorization(s) in electrical engineering 132
Matrix factorization(s) polar decomposition 445
Matrix factorization(s) rank 135
Matrix factorization(s) rank-revealing 445
Matrix factorization(s), Cholesky 417 445
Matrix factorization(s), complex eigenvalue 309
Matrix factorization(s), diagonal 289 300
Matrix factorization(s), LU 128
Matrix factorization(s), modified QR 366
Matrix factorization(s), orthogonal diagonalization 406
Matrix factorization(s), permuted LU 132
Matrix factorization(s), QR 135
Matrix factorization(s), reduced LU 135
Matrix factorization(s), Schur 402
Matrix factorization(s), similarity 301
Matrix factorization(s), singular value decomposition 135 426 430
Matrix factorization(s), spectral 135
Matrix for T relative to bases 297 298
Matrix inversion 113—114
Matrix multiplication 71; see also “Composition of linear transformations”
Matrix multiplication, definition of 99
Matrix multiplication, properties of 102
Matrix notation see “Back-substitution”
Matrix of coefficients see “Coefficient matrix”
Matrix of observations 436
Matrix transformation 72 80
Matrix-vector product 48
Matrix-vector product, properties of 52
Mean square error 399
Mean-deviation form 378
Migration matrix 88 260 286
Minimal realization 134
Minimum length solution 445
Modified QR factorization 366
Molecular modeling 152
Moore — Penrose inverse 433
Muir, Thomas 161
Multichannel (multispectral)image 403 439
Multiple regression 380
Multiplicative property of det 172 284
Multiplicity 283
Multivariate data 438
National Geodetic Survey 331
Negative (of a vector) 191
Negative definite quadratic form 416
Negative flow, in a network branch 27
Negative semidefinite form 416
Network, branch currents 31—32
Network, branches 25
Network, flow 25
Network, junctions (nodes) 25
Noise, random 257
Nonhomogeneous linear difference equation 251 254
Nonhomogeneous system 59
Nonlinear dynamical system, n Nontrivial solution 58 65
Nonzero column 13
Nonzero row 13
Nonzero singular number, smallest 433
Norm of a vector 334 386;
Normal equations 332 368
Normal equations, ill-conditioned 371
Normalized vectors 345
Normalizing a vector 335
North American Datum (NAD) 331
nth-order Fourier approximation 398
Null space (of a matrix) 200; see also “Fundamental subspaces” “Kernel”
Null space (of a matrix) contrast with column space 204 206
Null space (of a matrix) explicit description 202
Null space (of a matrix) implicit description 202
Null space (of a matrix), basis for 214
Null space (of a matrix), dimension of 233 238
Observation vector 376 436
Observed y-value 376
Ohm's law 27 133
Ohms 27
Oil exploration 2
One-to-one linear transformation 83 85 218 223;
One-to-one mapping 82—83
Onto mapping, Si 83 5
Orbit of a comet 382
Ordered basis 220
Ordered n-tuples 41
Ordered pairs (of real numbers) 38
Orthogonal basis 343 407
Orthogonal basis, Gram — Schmidt process 359
Orthogonal complement 338
Orthogonal decomposition 353
Orthogonal distances, sum of, squares of 444
Orthogonal eigenvectors 406
Orthogonal matrix 346 405
Orthogonal polynomials 388
Orthogonal projection 352
Orthogonal projection, geometric interpretation 348 354
Orthogonal projection, matrix for 357
Orthogonal projection, onto a subspace 353
Orthogonal projection, onto Span {u} 347
Orthogonal projection, properties of 355
Orthogonal projection, sum of 349
Orthogonal regression 444
Orthogonal set 342
Orthogonal vectors 338 386
Orthogonal'Decomposition Theorem 353 387
Orthogonality 338
Orthogonally diagonalizable matrix 406
Orthonormal, basis 344 357 362
Orthonormal, columns 345
Orthonormal, matrix 346
Orthonormal, rows 346
Orthonormal, set 344
Outer product 106 123
Overdetermined linear system 24
Parallel line(s) 57—58 60
Parallel processing 2 105
Parallel solution sets 6
| Parallelogram law, for vectors 341
Parallelogram rule for addition 40
Parallelograms of equal area 180
Parameter vector 376
Parametric, descriptions 20
Parametric, equation of line 57
Parametric, equation of plane 59
Parametric, vector form 59 61
Partial pivoting 18
Partitioned matrix 121
Partitioned matrix, inverse of 124
Pauli spin matrices 158
Permuted lower triangular matrix 131
Permuted LU factorization 132
Perpendicularity see “Orthogonality”
Perspective projection 154
Phase, backward 18 129
Phase, forward 18
Pivot(s) 15—16 281
Pivot(s), column(s) 14 17 22 24 215 A-1
Pivot(s), position(s) 14
Plane 59
Plane, implicit description of 59
Plane, parametric equation of 59
Plane, spanned by two vectors 43
Plane, translated 63
Point masses 47
Polar coordinates A-6
Polar decomposition 445
Polynomial(s), characteristic 283 286
Polynomial(s), degree of 193
Polynomial(s), Hermite 234
Polynomial(s), interpolating 35 158
Polynomial(s), Laguerre 234
Polynomial(s), Legendre 393
Polynomial(s), orthogonal 388
Polynomial(s), trigometric 397
Polynomial(s), zero 193
Population dynamics 271
Population movement 87—90
Position vector 56
Positive definite matrix 417
Positive definite quadratic form 416
Positive semidefinite matrix 417
Power method 321
Powers of a matrix 104
Predator-prey system 311
Predicted y-value 376
Price equation 148
Price vector 148
Principal axes 414
Principal Axes Theorem 414
Principal component analysis 404 436 439
Principal component(s) 439
Principal component(s), first 439
Principal component(s), second 439
Probability vector 259 268
Process control data 436
PRODUCT see also “Column-row expansion of AB” “Inner
Product of complex numbers A-7
Product of elementary matrices 117
Product of matrices 99
Product of matrix inverses 111
Product of matrix transposes 105
Product, dot 333
Product, matrix-vector 48
Product, outer 106 123
Product, scalar 106
Production equation 144
Production vector 143
Projection matrix 409 410;
Projection transformation 158
Properties of  41
Properties of Determinants Theorem 282
Properties, determinants 168 282
Properties, matrix addition 98
Properties, matrix inversion 110
Properties, matrix multiplication 102
Properties, matrix-vector product Ax 52
Properties, orthogonal projections 355
Properties, transpose 104
Pseudoinverse (Moore — Penrose, inverse) 433 445
Public work schedules budget constraint 424
Public work schedules feasible set 424
Public work schedules indifference curve 424
Public work schedules utility 424
Pure imaginary numbers A-5
Pythagorean Theorem 389
QR algorithm 286 287
QR factorization 135 363 365 371
QR Factorization Theorem 363
QR factorization, modified 366
Quadratic form(s) 441
Quadratic form(s), indefinite 416
Quadratic form(s), negative definite 416
Quadratic form(s), positive definite 416
Quadratic Forms and Eigenvalues Theorem 416
Quadratic trend 395
Range (of a transformation) 72 203 207
Rank 235 238—241; “Outer “Spectral
Rank in control systems 270
Rank theorem 238
Rank, effective 241 429
Rank, estimation 429
Rank, factorization 135
Rank, full 242
Rank, Invertible Matrix Theorem 240
Rank, properties of 269
Rank-revealing factorization 445
Rayleigh quotient 328
Real axis A-5
Real numbers 2
Real numbers, ordered pairs of 38
Real part, complex number A-3
Real part, complex vector 306
Real vector space 191
Rectangular coordinate system 38
Recurrence relations see “Difference equations”
Recursion relation 253
Reduced echelon form 13 21 203 237
Reduced echelon form, unique 14
Reduced LU factorisation 135
Reduced singular value, decomposition 433
Reflection 84
Reflection, Householder 158
Regression coefficients 376
Regular stochastic matrix 264
Renter of projection 154
Residual vector 378
Resistance 27
Right distributive law 102
Right singular vectors 430 442
Right-multiplication 176
RLC circuit 218
Rotation due to a complex eigenvalue 308—309
Rotation transformation 76 81 93 151 156
Row echelon form 13; see also “Matrix (matrices)”
Row equivalent matrices 7 19 44
Row Operations Theorem 368
Row operations, elementary 7
Row operations, replacement 7 173
Row operations, reversible 7
Row operations, scaling 7 173
Row reduced 14
Row reduction 22 47 111
Row reduction algorithm 13 16
Row reduction algorithm, backward phase 18 129
Row reduction algorithm, forward phase 18
Row space (of a matrix) 235; see also “Fundamental subspaces”
Row space (of a matrix), basis for 236
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