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| Авторизация |
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| Usmani R.A. — Applied Linear Algebra |
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| Предметный указатель |
Absolute convergence 181
Adjoint of a matrix 42 171
Analytic 183
Applications of positive definite matrices 165
Augmented matrix 40f 216
Band matrices 45
Basis of a vector space 16
Binary operation 1f
Cauchy — Schwarz inequality 24
Cayley — Hamilton theorem 156 170
Change of basis 118
Characteristic equation 123
Characteristic value see "Eigenvalue"
Characteristic vector see "Eigenvector"
Chebib, F. 78
Choleski's decomposition 207
Cofactor 41
Column rank 56
Conjugate transpose 84
Consistent system 82f 91 216
Cramer's rule 216 220
Determinant 212
Difference equation 46 156 206
Differential equation 132 185
Differentiation of a matrix 183
Dimension of a vector space 16
Discretization error 207
Eigenvalue 123
Eigenvalues of a band matrix 135
Eigenvalues of a circulant matrix 140
Eigenvalues of a companion matrix 138
Eigenvector 123
Elementary column operations 40
Elementary matrices 62
Elementary row operations 40
Error equation 207
Exp (A) 182 187
Factor analysis 167
Fibonacci sequence 160
Field 1
Finite difference method 206
Finite field 3
Fischer, C.F. 48
Full column rank 83
Full rank factorization 93
Full row rank 88
Functions of a matrix 170f
Gauss — Jordan reduction 40f 217
Generalized eigenvectors 150f
Generalized inverse 65f
Gershgorin theorem 162
Goldberg, S. 158
Graph of a matrix 197
Graph of a matrix, strongly connected 197
Greville, T.N.E. 71
Henrici, P. 203 209
Hermitian matrix 88 128
Homogeneous linear equations 60f
Inconsistent system 82 216
Index of  176
Inner product 23 143
Integration of a matrix 183
Inversion of a matrix 37
Isomorphism 104
Jordan's block 149 176
Jordan's box 149
Jordan's canonical form 149f 175f
Kantorovich, L.V. 211
Konig, D. 198
Kuttler, J.R. 204
l'Hopital's rule 5f
Laplace methods of expanding determinant 46 124f
Laplace transform method 187
Lawson, C.L. 79 167
Least squares solution 81f
Left inverse 65f
Linear dependence 16 126
Linear difference equations see "Difference equation"
Linear differential equations see "Differential equation"
Linear equations 12f 39 214
Linear transformation 101f
Linear transformation, null of 103
Linear transformation, perpendicular projection of 103
Linear transformation, range of 103
Linear vector space see "Vector space"
Marsden, M.J. 209
Matrix 9
Matrix of a linear transformation 108
Matrix, adjoint 42
Matrix, band 45
Matrix, circulant 140
Matrix, companion 113 138
Matrix, defective 132
Matrix, diagonal 9 43
Matrix, diagonally dominant 200
Matrix, elementary 62
Matrix, five-band 51 202
| Matrix, hermitian 58 128
Matrix, identity 9
Matrix, irreducible 194
Matrix, lower triangular 43
Matrix, monotone 194 202
Matrix, negative definite 160
Matrix, nilpotent 181
Matrix, nonnegative 198
Matrix, nonsingular 38
Matrix, null 10
Matrix, orthogonal 145 147
Matrix, permutation 1
Matrix, positive definite 160
Matrix, reducible 194
Matrix, scalar 9
Matrix, singular 38
Matrix, skewsymmetric 34
Matrix, square 9
Matrix, symmetric 34
Matrix, unit 9
Matrix, upper triangular 43
Matrix, zero 10
Meek, D.S. 230
Minimum polynomial 172f
Monic polynomial 172f
Moore — Penrose inverse 84
Newton's method 210
Noble, B. 42
Norm 22
Norm of a matrix 22
Norm of a vector 22
Null space of a matrix 60
One-2-3 inverse 84
One-2-4 inverse 84
One-inverse 84f
Orthogonal matrix 147f
Orthogonal set of vectors 143
Partitioning 31 194
Perron — Frobenius theorem 199
Plate deflection theory 209
Polynomial, characteristic 124f
Polynomial, minimum 172
Polynomial, monic 172
Positive definite matrix 160
Power series 179
Principle of least squares 72f
Principle of Mathematical Induction 39 115 138 144 147 150 157
Product of two linear transformations 115
Proper value see "Eigenvalue"
Proper vector see "Eigenvector"
Pseudo-inverse 84
Range of a matrix 63
Rank of a matrix 56
Rational function 3
Reduced column echelon form 55
Reduced row echelon form 55 217
Reflection 106
Relative maxima 74
Relative minima 74
Right inverse 65f
Rotation of plane 102
Rounding errors 208
Row equivalent matrix 54
Row rank of a matrix 56
Rutherford, D.E. 49 228
Scatter diagram 73
Sequence of matrices 179
Set 1
Shoosmith, J.N. 205
Similar matrices 120
Skew-Hermitian 88
Spanning set 15
Spectral radius 180
Spectral theorem 143f
subspace 13
Subspace, column space 54f
Subspace, null space 60
Subspace, row space 54f
Substitution, back 207
Substitution, forward 207
Sylvester theorem 177
Trace 35
Transition matrix 115f
Transposition 34
Two-point boundary value problem 205
Two-point boundary value problem, linear 205f
Two-point boundary value problem, nonlinear 209f
Usmani, R.A. 48 53 78 209 230
Vandermonde matrix 118
Varga, R.S. 198 199
Vector space 4
Vector space, basis of a 16f 18
Vector space, dimension of a 16f 18
Vector, column 9
Vector, row 9
Weak row sum criterion 203
Wronskian determinant 21
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