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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

$\mathbb{R}^2$       38
$\mathbb{R}^n$       45
$\mathrm{C}[a, b]$       198
$\mathrm{M}_{m \times n}$       198
$\mathscr{B}$ -coordinate vector      220 299
$\mathscr{B}$ -matrix, compute      301
(i,j)-cofactor      164
(i,j)-entry      97
Accelerator-multiplier model      257
Adjugate      179
Affine transformation      79
Algebraic multiplicity of an eigenvalue      283 287
Algebraic properties of $\mathbb{R}^n$       41
Algorithm bases for Col A, Row A, Nul A      236—237
Algorithm for finding $\mathrm{A}^{-1}$       113
Algorithm, compute a $\mathscr{B}$ -matrix      301
Algorithm, diagonalization      290—291
Algorithm, finding change-of-coordinates matrix      246
Algorithm, Gauss — Seidel method      139
Algorithm, Gram — Schmidt process      360—362
Algorithm, implementing diagorialization theorem      290
Algorithm, inverse power method      326
Algorithm, Jacobi's method (iterative, solution)      137
Algorithm, Jacobi's method for eigenvalues      286
Algorithm, LU factorization      130
Algorithm, QR algorithm, row-column rule for computing AB      101
Algorithm, row reduction      16—17
Algorithm, rule for computing Ax      52
Algorithm, solve a linear system      22
Algorithm, steady-state vector      264
Algorithm, write solution set in parametric vector form      61
amps      27
Analysis of data      128; see also “Matrix factorization(s)”
Analysis of variance      369
Angles in $\mathbb{R}^2$ and $\mathbb{R}^3$       339
Anticommute (matrices)      158
Area of parallelogram      180
Area of triangle      185
Argument of complex number      307 A-6
Associative law for multiplication      102
Associative property of addition      98
Augmented matrix      5
Auxiliary equation      253
Average value      390
Axioms, inner product space      384
Axioms, vector space      19128
Back-substitution      21 372
Backward phase      18
Basic variable      19
Basis for eigenspace      275 293
Basis, change of      243 245
Basis, change of, in $\mathbb{R}^n$       246
Basis, Col A      215
Basis, coordinates relative to      220
Basis, eigenvector, for $\mathbb{R}^n$       289 300
Basis, Nul A      214
Basis, ordered      220
Basis, RowA      236 237
Basis, solution space      254
Basis, standard      212
Bessel's inequality      401
Best approximation in $\mathbb{P}_n$       388
Best approximation in $\mathrm{C}[0,2 \pi]$       398
Best approximation in inner product spaces      387
Best approximation theorem      355
Best approximation to y by elements of W      355
Bill of final demands      see “Final demand vector”
Block diagonal matrix      125
Block matrix      see “Partitioned matrix”
Block upper triangular (matrix)      124 126
Bound vector      56
boundary conditions      257
Branch currents      28
Branches in network      25
Budget constraint      424
Cambridge Diet      37 86
Casorati matrix      250
Casoratian      250
Cauchy — Schwarz inequality      389
Cauchy, Augustin-Louis      161
Cayiey — Hamilton theorem      329
Center of gravity (mass)      47
Change of basis      243 245
Change of basis, in $\mathbb{R}^n$       246
Change of variable in a quadratic form      412
Change of variable in principal component analysis      440
Change of variable, decoupling a system of difference equations      316
Change of variable, eliminating cross-product term      412
Change-of-coordinates matrix      223 245—246 298 300
Characteristic equation      282 303
Characteristic polynomial      283 286
Characterization of Linearly Dependent Sets Theorem      66
Cholesky factorization      417
Classical adjoint      see “Adjugate”
Coefficient matrix      5 51
Coefficient(s), decimal      35
Coefficient(s), filter      251
Coefficient(s), matrix      5 51
Coefficient(s), regression      376
Coefficient(s), trend      396
Cofactor expansion      164
Colinear (vectors)      see “Linearly dependent set”
Column space (of a matrix)      203; see also “Fundamental subspaces” “Rank”
Column space (of a matrix), basis for      215
Column space (of a matrix), contrast with null space      204 206
Column space (of a matrix), dimension of      233 238
Column vector      38
Column(s) operations      171
Column(s) sum      145
Column(s), set spanned by      51
Column(s)span $\mathbb{R}^m$       51
Column-row expansion of AB      124
Commute      103
Commuting matrices      103
Companion matrix      256 330
Complex conjugate of a complex, vector      306
Complex eigenvalue(s)      283 304 306 317 318
Complex eigenvalue(s), conjugatae pairs      307
Complex eigenvector(s)      304
Complex numbed system      A-3
Complex numbed system and $\mathbb{R}^2$       A-7
Complex number(s)      38 A-3
Complex number(s), absolute value (modulus)      A-4
Complex number(s), argument of      A-6
Complex number(s), conjugate      A-4
Complex number(s), imaginary part of      A-3
Complex number(s), multiplicative inverse      A-4
Complex number(s), polar coordinates      A-6
Complex number(s), product of      A-7
Complex number(s), quotient of      A-7
Complex number(s), real axis      A-7
Complex number(s), real part of      A-3
Complex root      253 283 303; “Complex
Complex vector space      191 303
Complex vector(s), complex conjugate of      306
Complex vector(s), imaginary part of      306
Complex vector(s), real part of      306
Component of y orthogonal to u      347
Composition of linear, transformations      99 133
Composition of mappings      98 151
Computer graphics      148
Computer graphics, 3D graphics      152
Computer, Mark II      1
Computer-aided design (CAD)      95
Computer-aided manufacturing (CAM)      95
Condition number      433
Condition number, singular value decomposition      432
Conformable for block, multiplication      122
Conjugate pairs of eigenvalues      307
Conjugate, of complex number      A-4

Consistent equation (system)      4 22 51 60—61
Constant of adjustment, positive      257
Constrained optimization problem      419
Consumption matrix      144
Continuous dynamical systems      272
Contraction      75
Contrast between Nul A and Col A      204 206
control systems      127 189 270 311
Control systems, control (or input) sequence      270
Control systems, controllable      270
Control systems, pitch control      190
Control systems, Schur complement      127
Control systems, space shuttle      189
Control systems, state vector      270
Control systems, state-space model      270
Control systems, steady-state response      311
Control systems, system matrix      127
Control systems, transfer function      127
Controllable (pair of matrices)      270
Convergent sequence      137 265 286 323 326
Coordinate mapping      223
Coordinate vector      220
Coordinates of x (relative to a basis)      220
Cost as a vector      45
Counterexample      70
Covariance      340 438
Covariance matrix      437 442
Cramer's rule      177
Cross-product term      412
Crystal      161 227
Crystallography      221
Current flow      27
Current law      27
De Moivre's theorem      A-7
Decomposing a force into component, forces      349
Decouple (a dynamical system)      288 316
Degenerate line      78
Degree (of a polynomial)      193
Design matrix      376 780 381
DET      108
Determinaat(s)      108 162—163 281
Determinaat(s) as a product of pivots      170 281
Determinaat(s) as a volume      182 281
Determinaat(s), characteristic equation      282
Determinaat(s), cofactor expansion      164
Determinaat(s), column operations      171
Determinaat(s), computer evaluation      171
Determinaat(s), formula for $3 \times 3$ matrix      167
Determinaat(s), geometric property      182
Determinaat(s), linearity property      172
Determinaat(s), multiplicative property      172 284
Determinaat(s), properties      282
Determinaat(s), recursive definition of      163
Determinaat(s), row operations      168
Diagonal entries (in a matrix)      106 289
Diagonal matrix      106 288
Diagonal Matrix Representation Theorem      300
Diagonalizable matrix      106 288
Diagonalizable matrix, distinct eigenvalues      292
Diagonalizable matrix, nondistinct eigenvalues      293
Diagonalizable matrix, orthogonally      406
Diagonalization theorem      289
Difference equation(s)      90 249 251; “Markov
Difference equation(s), Casorati matrix      251
Difference equation(s), dimension of solution space      254
Difference equation(s), eigenvectors      278
Difference equation(s), filter coefficients      251
Difference equation(s), first order      89 255 259 272 278 284
Difference equation(s), fundamental set of solutions      254
Difference equation(s), general solution      254
Difference equation(s), homogeneous      251
Difference equation(s), linear filter      251
Difference equation(s), nonhomogeneous      251 254
Difference equation(s), order n      251
Difference equation(s), reduction to first order      255
Difference equation(s), solution set      253
Differential equations      207—208 218 249 272
Differential equations, and Laplace transforms      127 178
Dilation      75 273 276
Dimension(s)      230
Dimension(s), classification of subspaces      231
Dimension(s), spatial      437
Dimension(s), spectral      437
Direction of greatest attraction      314 317
Direction of greatest repulsion      314 316
Discrete linear dynamical system      see “Dynamical system”
Discrete-time signals      see “Signals”
Distance between vector and subspace      348 356
Distance between vectors      336 386
Distributive laws      102
Domain (of transformation)      72
Dot product      333
Dynamical system      271 284 310; “Stage-matrix
Dynamical system, attractor      314
Dynamical system, change of variable      315
Dynamical system, complex eigenvalues      306 317
Dynamical system, decouple      288 316
Dynamical system, graphical description      313
Dynamical system, long-term behavior      310
Dynamical system, nonlinear      314
Dynamical system, predator-prey      311 320
Dynamical system, repeilor      314
Dynamical system, saddle point      315
Dynamical system, spotted owl      271 311 318
Dynamical system, trajectory      313
Echelon form      13 22
Echelon form of matrix A      14
Echelon matrix      13
Effective rank      241 429
Eigenspace      274
Eigenspace, one-dimensional      292
Eigenspace, orthogonal basis for      407
Eigenvalue(s) of a real matrix that acts on $\mathbb{C}^n$       307
Eigenvalue(s), algebraic multiplicity      283
Eigenvalue(s), complex      283 304
Eigenvalue(s), inverse power method      325
Eigenvalue(s), power method      321
Eigenvalue(s), Rayleigh quotient      328
Eigenvalue(s), Spectral Theorem      408
Eigenvalue(s), spectrum      408
Eigenvalue(s), strictly dominant      321
Eigenvalue(s), zero      277
Eigenvector(s)      273
Eigenvector(s) of a real matrix that acts on $\mathbb{C}^n$       307
Eigenvector(s), basis for $\mathbb{R}^n$       289 300
Eigenvector(s), complex      304
Eigenvector(s), decomposition      285 311 322
Eigenvector(s), difference equations      278
Eigenvector(s), orthogonal      406
Eigenvector(s), principal axes      4 4
Elastic beam      109
Electrical network      2 27 132 134 136 218
Elementary matrix      111
Elementary reflector      401
Elementary row operations      7
Equal matrices      97
Equal vectors      38 191
Equation(s), auxiliary      253
Equation(s), consistent      4 50
Equation(s), inconsistent      4 9 25 54
Equation(s), matrix      38 49
Equation(s), normal      332 368
Equation(s), parametric      57 59
Equation(s), three-moment      257
Equation(s), vector      38 49
Equilibrium prices      29
Equilibrium, unstable      320
Equivalence relation      301
Equivalent linear systems      3
Evolution      see “Long-term behavior”

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