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Lay D.C. — Linear Algebra And Its Applications

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Название: Linear Algebra And Its Applications

Автор: Lay D.C.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 503

Добавлена в каталог: 07.06.2008

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Предметный указатель

Exchange model      29
Existence and uniqueness theorem      22
Existence questions      8 21 50 73 81
Explicit description      59
Explicit description of NuM      202
Factorization(s)      see also “Matrix factorization(s)” “Singular
Factorization(s) for analyzing a dynamical system      288
Factorization(s) in electrical engineering      132—134
Factorization(s) of block matrices      126
Factorization(s), modified QR      366
Factorization(s), Schur      402;
Feasible set      424
Filter coefficients      251
Filter, linear      251
Filter, low-pass      252 374
Final demand vector      143
Finite-dimensional (vector space)      230
Finite-dimensional (vector space), subspaces of      232
First principal component      439
First-order difference equation      see “Difference equation(s)”
Flexibility matrix      109
Force, decomposition of      349
FORTRAN      53
Forward phase      8
Fourier approximation, nth-order      398
Fourier coefficients      398
Fourier series      399
Free variable(s)      19 48;
Free vector      56
Full rank (matrix)      242
Function      see “Transformation”
Fundamental set of solutions      254
Fundamental subspaces (of a matrix)      239 242 339 401 433
Gauss — Seidel method      139
Gauss, Carl Friedrich      13 383
Gaussian elimination      13
General least-squares problem      366
General linear model      378
General solution      19 59 254
Geometric descriptions of $\mathbb{R}^2$       39
Geometric descriptions of Span {u,v}      43
Geometric descriptions of Span {v}      43
Geometric point      39
Givens rotation      93
Gram matrix      445
Gram — Schmidt process      359 363 365 386
Gram — Schmidt process in $\mathbb{P}_n$       387 396
Gram — Schmidt process in $\mathbb{R}^n$       359 363
Gram — Schmidt process in $\mathrm{C} (0,1]$       391
Gram — Schmidt process in inner product spaces      386
Gram — Schmidt Process Theorem      362
Gram — Schmidt process, Legendre polynomials      393
Graphics workstations      155
Helmert blocking strategy      332
Hermite polynomials      234
Homogeneous coordinates      150 152
Homogeneous linear difference equation      see “Difference equation(s)” “Kernel”
Homogeneous system      58
Hooke's law      109
Householder, matrix      401
Householder, reflection      158
Hyperspectral image processing      442
Identity for matrix multiplication      102
Identity matrix      52 102 104
Ill-conditioned equations      371
Image (of vector)      72
Image processing, hyperspectral      442
Image processing, matrix of observations      436
Image processing, observation vector      436
Image processing, principal component analysis      439
Image processing, scatter plot      436
Image processing, spatial dimensions      437
Image processing, spectral dimensions      437
Imaginary axis      A-5
Imaginary numbers, pure      A-5
Imaginary part, complex number      A-3
Imaginary part, complex vector      306
Implicit definition of Nul A      202
Implicit description      59 269
Inconsistent system      see “Linear systems”
Indefinite quadratic form      416
Indifference curve      424
Infinite-dimensional (vector space)      230
Inner product      106
Inner product and angles      339
Inner product axioms      389
Inner product evaluation      390
Inner product on $\mathbb{P}_n$       385
Inner product on $\mathbb{R}^n$       333 385
Inner product on $\mathrm{C} [a,b]$       391
Inner product, properties      334
input sequence      see “Control systems”
Input-output model      29 144
Intermediate demand(s)      143
Interpolating polynomial      35 158
Intersection of subspaces      199
Invariant plane      309
Inverse (of a matrix)      107
Inverse (of a matrix) formula, using the adjugate      179
Inverse (of a matrix) of a $2 \times 2$ matrix      108
Inverse (of a matrix) of a partitioned matrix      124
Inverse (of a matrix) of a product      111
Inverse (of a matrix) of an elementary matrix      112
Inverse (of a matrix) of the transpose      111
Inverse (of a matrix), algorithm for finding      113
Inverse Formula Theorem      179
Inverse power method      325
Invertible linear transformation      119
Invertible matrices      107 110
Invertible Matrix Theorem      117 170 240 277
Isomorphic vector spaces      235
Isomorphism      224 225 254
Iterative methods, formula for $(\mathrm{I} - \mathrm{C})^{-1}$       146 148
Iterative methods, Gauss — Seidel      139
Iterative methods, Jacobi's method, eigenvalue estimate      286
Iterative methods, Jacobi's method, iterative solution      137
Iterative methods, QR algorithm      287
Jacobi's method for eigenvalues      286
Jacobian matrix      314
Jordan, Wilhelm      13
Kernel (of a linear transformation)      207
Kirchhoff current law      28 133
Kirchhoff voltage law      28 133
Ladder network      133
Laguerre polynomials      234
Lamberson, R.      272
Landsat images      403 436 439 442
Landsat satellites      403
LAPACK      125
Laplace transforms      127 178
Law of Cosines      339
Leading, entry      13
Leading, variables      19
Least-squares error      370 399;
Least-squares fit, cubic trend      380
Least-squares fit, linear trend      395
Least-squares fit, quadratic trend      379 395 397
Least-squares fit, scatter plot      379
Least-squares fit, seasonal trend      382
Least-squares fit, trend surface      380
Least-squares line      376
Least-squares line, observed y-value      376
Least-squares line, predicted y-value      376
Least-squares line, residual      376
Least-squares line, weighted      395
Least-squares plane      381
Least-squares solution(S)      333 367 434
Least-squares solution(S) alternative calculations      371
Least-squares solution(S) of minimum length      445
Least-squares solution(S), least-squares line      377

Least-squares solution(S), normal equations      368
Least-squares solution(S), North American Datum      332
Least-squares solution(S), unique      370 372
Least-squares, weighted      385 393
Left distributive law      102
Left singular vectors      430
Left-multiplication      111 176
Legendre polynomials      393
Leibnitz, Gottfried      161
Length of a vector      334 386
Leontief, exchange model      29
Leontief, input-output model      29 144
Leontief, production equation      144
Leontief, Wassily      1 142 148
Line degenerate      78
Line parametric equation      57
Line Span {u}      43
Line through p parallel to v      57
Line, translation of      56
Linear combination(s)      42 48 195
Linear combination(s) in applications      45
Linear combination(s), weights      42 48 203
Linear dependence in $\mathbb{R}^3$       67
Linear dependence relation      64 211 215
Linear difference equation(s)      see “Difference equation(s)”
Linear equation      2
Linear filter      251
Linear independence      63 211
Linear independence in $\mathbb{R}^n$       84
Linear independence in a space of polynomials      225
Linear independence in the space S of signals      249
Linear independence of matrix columns      65
Linear model      378
Linear programming      2 125
Linear recurrence relation      see “Difference equations”
Linear system(s)      3 44 49
Linear system(s) equivalent      3
Linear system(s) existence of solution(s)      8 21
Linear system(s) general solution(s)      19
Linear system(s) inconsistent      4 9 54
Linear system(s) infinitely many solutions      21—22
Linear system(s) row equivalent      8 19
Linear system(s) solution      3 19
Linear system(s) solution set(s)      3 20
Linear system(s) unique solution      22
Linear system(s) uniqueness questions      8
Linear system(s), basic strategy for solving      5
Linear system(s), coefficients for      2
Linear system(s), consistent      see “Consistent equation (system)”
Linear system(s), elimination procedure      5
Linear system(s), homogeneous      58
Linear system(s), iterative solutions of      137
Linear system(s), nonhomogeneous      59
Linear system(s), overconstrained      34
Linear system(s), overdetermined      24
Linear system(s), triangular form      6 12
Linear system(s), underconstrained      34
Linear system(s), underdetermined      24
Linear transformation(s)      74 80 253 296;
Linear transformation(s) contraction      75
Linear transformation(s) diagonal matrix representation      300
Linear transformation(s) similarity of matrix representations      300
Linear transformation(s) standard matrix      80
Linear transformation(s) superposition principle      75
Linear transformation(s), $\mathscr{B}$ -matrix      298 301
Linear transformation(s), composition of      99
Linear transformation(s), dilation      75 273 276
Linear transformation(s), Givens rotation      93
Linear transformation(s), Householder reflection      158
Linear transformation(s), invertible      119
Linear transformation(s), matrix for      80 297—298 301
Linear transformation(s), matrix relative to bases      297 298
Linear transformation(s), one-to-one      82—83 218 224
Linear transformation(s), onto      81 83
Linear transformation(s), range of      203
Linear trend      395
Linearity property of det      172
Linearly dependent set (vectors)      64 66—68 211
Linearly dependent set (vectors) by inspection      66
Linearly dependent set (vectors), characterization of      66 211
Linearly independent eigenvectors      289 291
Linearly independent set (vectors)      64 211;
Linearly independent set (vectors), column vectors      67 70
LINPACK      105
Long-term behavior, of a dynamical system      310
Long-term behavior, of a Markov chain      262 265
Loop      27
Low-pass filter      252 374
Lower triangular matrix      127 128
Lower triangular part      139
LU factorization      128 132 326 365
LU factorization, permuted      132
LU factorization, reduced      135
Maple      286
Mapping      see also “Transformation”
Mapping, coordinate      223
mapping, one-to-one      82
Mapping, onto $\mathbb{R}^m$       1 81
Marginal propensity to consume      257
Markov chain(s)      259 286 320;
Markov chain(s), steady-state vectors      263
Mass-spring system      198 218
Mathematica      286
Mathematical ecologists      271
Mathematical modeling      1—2
MATLAB      10 139 140 286 318 324 326 327 330
MATLAB exercises      11 33 35 91 135 141—142 320—321 327—328 330 374 382—383 442
Matrix (matrices) change-of-coordinates      223 245—246 298 300
Matrix (matrices) coefficient      5 51
Matrix (matrices) companion      256 330
Matrix (matrices) consumption      144
Matrix (matrices) covariance      437
Matrix (matrices) design      376 380 381
Matrix (matrices) effective rank      241 429
Matrix (matrices) flexibility      109
Matrix (matrices) identity      52
Matrix (matrices) in echelon form      13
Matrix (matrices) in reduced echelon form      13
Matrix (matrices) of a linear transformation      297 298
Matrix (matrices) of a quadratic form      441
Matrix (matrices) of cofactors      179
Matrix (matrices) of observations      436
Matrix (matrices) projection      409 410
Matrix (matrices) row equivalent      7 19
Matrix (matrices) unit lower triangular      128
Matrix (matrices) upper triangular      128
Matrix (matrices) zero      62 98
Matrix (matrices), $\mathrm{m} \times \mathrm{n}$       5 96
Matrix (matrices), (i,j)-entry in      97
Matrix (matrices), adjugate of      179
Matrix (matrices), anticommuting      158
Matrix (matrices), augmented      5
Matrix (matrices), block diagonal      125
Matrix (matrices), block upper triangular      124
Matrix (matrices), Casorati      250
Matrix (matrices), column space of      203
Matrix (matrices), commuting      103
Matrix (matrices), definition of      4
Matrix (matrices), determinant of      108
Matrix (matrices), diagonal      106 288
Matrix (matrices), diagonalizable      289
Matrix (matrices), echelon      13
Matrix (matrices), elementary      111
Matrix (matrices), equal      97
Matrix (matrices), Gram      445
Matrix (matrices), Householder      401
Matrix (matrices), inverse of      107
Matrix (matrices), invertible      107 110 117
Matrix (matrices), Jacobian      314
Matrix (matrices), left-multiplication      111 176

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