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| Авторизация |
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| Lay D.C. — Linear Algebra And Its Applications |
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| Предметный указатель |
Row space (of a matrix), dimension of 238
Row vector 235
Rule see “Algorithm”
Saddle point 315
Sample covariance matrix 437
Sample mean 437
Sample variance 443
Samuelson, P.A. 257
scalar 39
Scalar multiple(s) 38 97
Scalar multiple(s), in  41
Scalar product see “Inner product”
Scale a vector 336
Scatter plot 379 436
Scene variance 40
Schur complementary 462
Schur factorization 402
Series circuit 133
Shear transformation 74 149 156
Shunt circuit 133
Signal(s) 189 192 249
Signal(s), moving average 257
Signal(s), noise 257
Signal(s), sampled 192 249
Signal(s), vector space of 192
Similar matrices 284 301;
Similarity transformation 284
Singular value decomposition (SVD) 135 426 430
Singular value decomposition (SVD), condition number 432
Singular value decomposition (SVD), estimating matrix rank 429
Singular value decomposition (SVD), least-squares solution 434
Singular value decomposition (SVD), principal component analysis 442
Singular value decomposition (SVD), pseudoinverse 433 445
Singular value decomposition (SVD), reduced 433
Singular values 428
Singular vectors, left 430
Singular vectors, right 430 442
Size (of a matrix) 5
Solution set(s) 3 20 56 200 253
Solution(s) 3 252;
Solution(s), difference equation 252 278
Solution(s), differential equation 208
Solution(s), explicit description of 278
Solution(s), fundamental set of 254
Solution(s), homogeneous system 58 201
Solution(s), in parametric vector fdrm 59 61
Solution(s), linear system 3 19
Solution(s), minimum length 445
Solution(s), nonhomogeneous systems 59—60
Solution(s), nontrivial 58
Solution(s), trivial 58
Solution(s), zero 58
Space shuttle, U.S., control systems 189
Space shuttle, U.S., pitch control system 190
span 42 51
Span  42 196
Span {u,v} as a plane 43
Span {u}, orthogonal projection onto 347
Span {v} as a line 43
Spanning set 59 197 216;
Spanning Set Theorem 213
Spatial dimensions 437
Spectra Theorem 408
Spectral decomposition 409
Spectral dimensions 437
Spectral factorization 135
Spectrum 408
Spotted owl 271 311 318
Stage-matrix model 272 318 321
Standard basis 212 220 246
Standard matrix 80 296
Standard position 414
Star Wars 149
State vector 127 259 270
State-space 270 311;
Steady-state response, of a control, system 311
Steady-state vector(s) 263 265 273 286
Stiffness matrix 109
Stochastic matrix 259 268 273 320
Stochastic matrix, regular 264
Strictly diagonally dominant matrix 141
Strictly dominant eigenvalue 321
SubMatrix 270
Subset of  spanned by 42 197
Subspace Test 195
Subspace(s) 193; see also “Vector space”
Subspace(s) of 194 231
Subspace(s) of a finite-dimensional space 232
Subspace(s) of polynomials 194
Subspace(s), associated with a linear transformation 207
Subspace(s), associated with a matrix 239 242 443
Subspace(s), column space 203
Subspace(s), eigenspace 274
Subspace(s), fundamental 242 443
Subspace(s), intersection of 199
Subspace(s), null space 201
Subspace(s), of the space S of signals 253
Subspace(s), row space 235
Subspace(s), spanned by a set 195—197
Subspace(s), zero 194
Sum of the squares for error 383 393
Superposition principle 75
Surface rendering 155
Symmetric matrix 310 328 405 417 421
Synthesis of data 128; see also “Matrix multiplication”
System matrix 127
System of linear equations see “Linear system(s)”
Takakazu, Suki 161
Theorem, Best Approximation 355 387
Theorem, Cauchy — Schwarz Inequality 389
Theorem, Characterization of Linearly Dependent Sets 66 211
Theorem, Column-Row Expansion of AB 124
Theorem, Cramer's Rule 177
Theorem, de Moivre's A-7
Theorem, Diagonal Matrix Representation 300
Theorem, Diagonalization 289
Theorem, existence and uniqueness 22
Theorem, Gram — Schmidt Process 362
Theorem, Inverse Formula 179
Theorem, Invertible Matrix 117 170 240 277
Theorem, Orthogonal Decomposition 353 387
Theorem, principal axes 414
Theorem, Properties of Determinants 282
Theorem, Pythagorean 338
Theorem, QR Factorization 363
Theorem, Quadratic Forms and Eigenvalues 416
Theorem, rank 238
Theorem, Row Operations 168
Theorem, Singular Value Decomposition 430
| Theorem, Spanning Set 213
Theorem, Spectral Theorem for Symmetric Matrices 408
Theorem, Subspace Test 195
Theorem, Triangle inequality 389
Theorem, Unique Representation 219
Theorem, Uniqueness of the Reduced Echelon Form 14 A-1
Three-moment equation 257
Total variance 438
Total variance, fraction of 441
Trace 303 438
Trajectory 313
Transfer function 127
Transfer matrix 132
Transformation see also “Linear transformation”
Transformation, affine 79
Transformation, definition of 72
Transformation, domain of 72
Transformation, identity 298
Transformation, image of a vector x under 72
Transformation, linear 74
Transformation, range of 72
Transformation, rotation 76 81 151 156
Translation (by a vector p) 56
Translation (by a vector p) in homogeneous coordinates 150
Transpose (of a matrix) 04
Transpose (of a matrix), determinant of 172
Transpose (of a matrix), properties of 104
Trend analysis 396
Trend coefficients 396
Trend function 396
Trend surface 380
Triangle inequality 389
Triangular matrix 13 165
Trigonometric polynomial 397
Trigonometric polynomial, order n 387
Trivial solution 58
Uncorrelated variables 438 441
Underdetermined linear system 24
Unique Representation Theorem 219
Uniqueness of the reduced echelon, form 14 A-1
Uniqueness question 8 21 73 82
Unit cell 221
Unit consumption vector 143
Unit lower triangular matrix 128
Unit vector 335 386
Unstable equilibrium between two populations 320
Upper triangular matrix 124 128
Utility function 424
Value added vector 148
Vandermonde matrices 158 187 330
Variables, basic 19
Variables, free 19 20
Variables, leading 19
Variance 394 438
Vector addition 39 19
Vector addition, as translation 56
Vector equation 38 44 49
Vector space 189 191;
Vector space and differentia equations 208
Vector space axioms 191
Vector space of arrows 191
Vector space of discrete signals 192
Vector space of functions 193
Vector space of polynomials 192
Vector space, complex 191
Vector space, finite-dimensional 230
Vector space, infinite-dimensional 230
Vector space, real 191
Vector space, subset of 193
Vector subtraction 42
Vector sum 38
Vector(s) as points 39
Vector(s) bound 56
Vector(s) column 38 39
Vector(s) normalizing 335
Vector(s) observation 376 436
Vector(s) of values 387
Vector(s) parameter 376
Vector(s) price 148
Vector(s) production 143
Vector(s) space 189
Vector(s) unit 335 386
Vector(s) unit consumption 143
Vector(s) with arrows 39
Vector(s), definition of 38
Vector(s), distance between 336
Vector(s), equal 38
Vector(s), equilibrium see “Steady-state vector”
Vector(s), final demand 143
Vector(s), free 56
Vector(s), in  38
Vector(s), in 41
Vector(s), left singular 430
Vector(s), linearly independent 64 211
Vector(s), negative of 191
Vector(s), normalized 345
Vector(s), orthogonal 338 386
Vector(s), parallelogram law for 341
Vector(s), position 56
Vector(s), probability 259
Vector(s), residual 378
Vector(s), right singular 430
Vector(s), set of all multiples 41
Vector(s), steady-state 263 265 273 286
Vector(s), typical multiples 41
Vector(s), value added 148
Vector(s), zero 41
Vertex (vertices) 149
Vibration of a weighted spring 198 208 218
Viewing plane 153
Virtual reality 152
VLSI microchips 122
Voltage see also “Electrical network”
Voltage drop 27
Voltage in an inductance-capacitance circuit 208 218
Voltage law 28
Voltmeter 218
Volts 27
Volume, ellipsoid 185
Volume, parallelepiped 180 281
Volume, tetrahedron 185
Weighted least-squares 385 393
Weights 42 48
Weights as free variables 203
Wire-frame car model 95 149
Zero matrix 62 98
Zero polynomial 193
Zero solution 58
Zero subspace 194
Zero vectors) 41; see also “Zero polynomial”
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