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| Авторизация |
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| Поиск по указателям |
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| Nicholson W.K. — Linear Algebra with Applications |
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| Предметный указатель |
Absolute value of a complex number 467
Adjoint matrix 108 123
Adjoint matrix, formula for inverse 125
Al — Khowarizmi 475
Algorithm, Cholesky 291
Algorithm, diagonalization 262
Algorithm, Gaussian 12 17
Algorithm, Gram — Schmidt 275 434
Algorithm, matrix inversion 61
Algorithm, QR — Algorithm 300
Algorithm, simplex 496
Algorithm, tnangulatron 404
angle 156 431
Angle, between two vectors 431
Angle, cosine of 469
Angle, radian measure 469
Angle, sine ot 469
Angle, standard position 469
Approximation, best 325
Approximation, Fourier 462
Approximation, least squares 178 327
Approximation, theorem 438
Argument of a complcx number 470
Associated homogeneous 50
Back substitution 19 79
Basis 213
Basis of eigenvectors 262 441 445
Basis, existence of 221
Basis, ordered 371
Basis, orthogonal 273 433
Basis, standard 214 303
Bessel’s inequality 441
Best approximation theorem 325
Bilinear form 324
Binet formula 416
Binomial coefficients 243
Binomial coefficients, theorem 243
Block, diagonal matnx 67
Block, multiplication 52
Block, partition of a matrix 52
Block, triangular matnx 78 391
Block, triangulation theorem 402
Brown.J W 461
Cancellation for matnx muliiplication 64
Cancellation for vector addition 191
Cauchy inequaliiy 428
Cauchy — Schwarz inequality 165
Cauchy, A I. 428
Cayley — Hamilton theorem 407
Cayley. A 33 407
Centroid of a triangle 155
Change of basis matrix 380
Characteristic polynomial 253 306
Characteristic polynomial of a block triangular matrix 391
Characteristic polynomial of a differential equation 245
Characteristic polynomial of an operator 186
Characteristic value 251
Characteristic value, vector 251
Cholesky decomposition 290
Cholesky decomposition, algorithm 291
Churchill, R V 463
Circuit rule 29
Closed economy 91
Coefficient matnx 5 50
Coefficients of an equation of a linear combination 204
Coefficients of an equation of a polynomial 191
Column matnx 34
Column space 228
Commute 45
Companion matnx 120
Complcx linear algebra 302—310
Complcx plane 468
Complement of a subspace 395
Completing the square 475
Complex distance formula 468
Complex matnx 304
Complex number 465
Complex number, absolute value 467
Complex number, argument 470
Complex number, conjugate 467
Complex number, DeMoivre’s theorem 472
Complex number, fundamental theorem of algebra 477
Complex number, imaginary part 465
Complex number, inverse of 467
Complex number, modulus 467
Complex number, multiplication rule 471
Complex number, parallelogram law of addition 469
Complex number, plane 468
Complex number, polar form 470
Complex number, pure imaginary 465
Complex number, real part 465
Complex number, roots of unity 473 474
Complex subspacc 311
Component(s) of a vector 147
composition 365
Congruence 320
conic 25
Conjugate of a complex number 467
Conjugate transpose 304
Conjugate transpose of 304
Consistent and inconsistent 20
Consistent system ol'lincar equations 20
Constant term 1
Constant term, function 219
Constant term, matrix 5 50
Constant term, sequence 411
Constraints 482 486 489
containment 206
Contraction 351
Convergence of Fourier cense 463
Convergence of state vectors 101
Coordinate axes 147
Coordinate vectors 148
coordinates 147 372
Coordinates of a vector 372
Cosine of an angle 469
Cotactor 109
Cotactor, matrix 123
Cramer. G 127
Cramer’s Rule 127
Cross product 168
Dantzig, G 489
Davis, P J 439
Degree 191
Demand matnx 93
DeMoivre, A 472
DeMoivre’s Theorem 472
Dependent (linearly) 209
Descartes, Rene 187
Determinant 110
Determinant of block triangular matrix 118 391
Determinant of operator 386
Determinant, adjoini formula 125
Determinant, Cramer's rule 127
Determinant, formal definition 110
Determinant, Laplace expansion 110 111 136
Determinant, product theorem 120
Determinant, Vandcrmonde 134
Diagonal matrix 43 56
Diagonal matrix, operator 442
Diagonal matrix, orthogonally 283 445
Diagonal matrix, unitarily 308
Diagonalization 334—35
Diagonalization of a Hermitian matnx 110
Diagonalization of a matnx 262 310
Diagonalization of a quadratic form 114
Diagonalization of a system of differential equations 334—35
Diagonalization of an operator 441
Diagonalization, algorithm 262
Diagonalization, first order 244 331
| Diagonalization, general solution 246 17 336
Diagonalization, initial condition 245
Diagonalization, linear system 332
Diagonalization, orthogonal 283 441
Diagonalization, second order 245 131
Difference 16 188 191
Differential equations 244 331
Differential equations, boundary condition 245 336
Differential equations, characteristic polynomial 245
Dilation 35
DIMENSION 14
Dimension of a subspace 223
Dimension, theorem 357
Direct sum 195
Direct sum of invariant subspaces 97
Direction cosines 165
Direction vector 150
Discnminant 475
Distance 156 425 448
Distributive property 48
Dot product 44 270
Dot product of geometric vectors 157
Doubly stochastic matrix 105
Economic models 90
Eigenspace of a matnx 252
Eigenspace of an operator 392
Eigenvalues 251
Eigenvalues of a matrix 251
Eigenvalues of an operator 392
Eigenvalues, complex 301 306
Eigenvalues, dominant 298
Eigenvalues, multiplicity of 265 394
Eigenvalues, positive 289
Eigenvalues, power method for finding 298
Eigenvalues, real 256 444
Eigenvectors 251 306 392
Eigenvectors of a matrix 251
Eigenvectors of an operator 392
Eigenvectors, basis of 262 441 445
Eigenvectors, dominant 298
Eigenvectors, independent 262 441
Electrical network 29
Elementary, column operation 78
Elementary, matrix 68
Elementary, operation 6
Elementary, row operation 8 68
ellipse 317
entries 33
Equality of functions 192
Equality of geometric vectors 141
Equality of linear transformations 346
Equality of matrices 35
Equality of n-tuples 187
Equality of polynomials 192
Equality of sequences 411
Equations differential (see Differential equations)
Equations linear (see Linear equations)
Equilibrium condition 92
Equilibrium in 92
Equilibrium in an economic system 92
Equilibrium in an economic system, condition for 92
Equivalent 6
Equivalent matrices 238
Equivalent matrices, Euclidean space 187
Equivalent matrices, inner product 421
Equivalent matrices, system of linear equations 6
Evaluation map 352 359
Evaluation of a polynomial 201 260
Evaluation of a polynomial at a matrix 260
Evaluation of a polynomial at the shift operator 417
Even polynomial 219
Even polynomial, function 462
Expansion theorem 273 433
Exponent law 471
Exponent law, bounded 486
Exponent law, bounding hyperplane 486
Exponent law, comer point 486
Exponent law, feasible region 482 486
Exponent law, lactor theorem 239
Extreme point 486
Extreme point, Binet, formula 416
Extreme point, Fibonacci sequence 416
Extreme point, generalized 419
Finite dimensional 214
Fixed line 452
Fixed line, axis 459
Fixed line, Hows in a network 27
Fixed line, hyperplane 458
Fixed line, plane 456
Fixed line, vector 459
Formula 156 468
Forward substitution 79
Fourier approximation 462
Fourier approximation, coefficients 433 461
Fourier approximation, series 463
Fourier, J B J 433
Function 192 339
Function, action of 192
Function, constant 219
Function, continuous 422
Function, differentiable 202
Function, distance preserving 460
Function, even/odd 462
Function, linear transformations 339
Function, objective 482 486 489
Function, pointwise operations 192
Fundamental identities 367
Fundamental theorem of algebra 477
Fundamental theorem of vector spaces 212
Gass. S 1 481 492
Gauss, K F 17 477
Gaussian algorithm 12 17
Gaussian algorithm, elimination 10 13
Generalized 402
Generalized inverse 325 31
Geometric vector 141
Gram — Schmidt algorithm 275 4 4
Gram, J P 275
Group of operators 460
Half plane 482
Hamilton, W R 407
Hcrstein, I N 408
Hcssenberg form 301
Hermite, C 305
Hermitian matrix 105
Homogeneous system of equations 24
Homogeneous system of equations, associated 50
Hooke's law 184 249
Householder matrices 301
Hyperbola 317
Hyperbola, idempotent matrix 56 68
Hyperbola, operator 401
Identity, linear transformation 343
Identity, matrix 45
Image of a linear transformation 351 352
Imaginary, axis 468
Imaginary, part of a complex number 465
Imaginary, unit 465
Inconsistent system 20
Independent (linearly) 209
Indeterminate 192
Index of a quadratic form 321
Induction, hypothesis 503
Induction, mathematical 501 502
Inequality, Bessel's 441
Inequality, Cauchy 428
Inequality, Cauchy — Schwarz 165
Inequality, Schwarz 427
Inequality, triangle 165 428 468
Initial point 141
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