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Schott J.R. — Matrix Analysis for Statistics
Îáñóäèòå êíèãó íà íàó÷íîì ôîðóìå Íàøëè îïå÷àòêó?
Íàçâàíèå: Matrix Analysis for StatisticsÀâòîð: Schott J.R. Àííîòàöèÿ: A complete, self-contained introduction to matrix analysis theory and practice
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 1996Êîëè÷åñòâî ñòðàíèö: 431Äîáàâëåíà â êàòàëîã: 21.10.2010Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
Ïðåäìåòíûé óêàçàòåëü
Moore — Penrose inverse 171 Moore — Penrose inverse and projection matrices 172—173 Moore — Penrose inverse and quadratic form in normal random vectors 179—180 Moore — Penrose inverse and rank 175 Moore — Penrose inverse and singular value decomposition 172 Moore — Penrose inverse and spectral decomposition 176—177 Moore — Penrose inverse of a matrix product 180—185 Moore — Penrose inverse of a sum 186—187 Moore — Penrose inverse of a symmetric matrix 176—178 Moore — Penrose inverse of block diagonal matrix 186 Moore — Penrose inverse of diagonal matrix 177 Moore — Penrose inverse of partitioned matrices 185—186 Moore — Penrose inverse, computation of 175 197—199 Moore — Penrose inverse, continuity of 188—190 Moore — Penrose inverse, derivative of 333—334 336—337 Moore — Penrose inverse, existence of 171—172 Moore — Penrose inverse, properties 174—180 Moore — Penrose inverse, uniqueness of 171—172 Multicollinearity 96—98 136 Multinomial distribution 368 Multiplicity of an eigenvalue 86 Multivariate normal distribution 25—26 331—332 347—349 Negative definite matrix 16 Negative semidefinite matrix 16 Nilpotent matrix 127 Nonnegative definite matrix 16 Nonnegative definite matrix, correlation matrix 24 Nonnegative definite matrix, covariance matrix 23 Nonnegative matrix 288 Nonnegative matrix, irreducible 294—295 Nonnegative matrix, irreducible, eigenvalues of 296—298 Nonnegative matrix, irreducible, eigenvectors of 296—297 Nonnegative matrix, primitive 298 Nonnegative matrix, spectral radius of 288 Nonsingular matrix 8 Norm, matrix 157—162 Norm, vector 35 37—38 Normal distribution, multivariate 25—26 331—332 347—349 Normal distribution, singular 26 379 Normal distribution, univariate 20 Normalized vector 14 Null matrix 2 Null space 60—61 Null vector 2 One-way classification model, multivariate 119—122 154 406—407 One-way classification model, univariate 79—80 119 228—229 231—232 257—258 385—387 396—397 Order of a minor 13 Order of a square matrix 1 Orthogonal complement 52 Orthogonal complement, dimension of 52 Orthogonal matrix 14—15 Orthogonal vectors 14 Orthonormal basis 48—52 Orthonormal vectors 14 Partitioned matrix 11—13 Partitioned matrix, determinant of 249—250 Partitioned matrix, inverse of 247 Partitioned matrix, rank 46—47 Pearson's chi-squared statistic 411 Permutation matrix 15 Perturbation methods 337—344 Perturbation methods, eigenprojection 343—344 Perturbation methods, eigenvalue 339—343 Perturbation methods, matrix inverse 338—339 Poincare separation theorem 111 Polar coordinates 17 Positive definite matrix 15—16 Positive matrix 288 Positive matrix, eigenvalues 289—294 Positive matrix, eigenvectors 289—293 Positive matrix, spectral radius 288 Positive semidefinite matrix 15—16 Primitive matrix 298 Principal components analysis 107—108 404 Probability function 18 Projection (orthogonal) 50 Projection matrix 52—59 QR factorization 140 Quadratic form 15—16 Quadratic form and Moore — Penrose inverse 179—180 Quadratic form, distribution of 378—384 Quadratic form, expected value of 390—398 Quadratic form, generalized 399 Quadratic form, independence of 384—390 Random variable 18—22 Random vector 22—26 RANGE 43 Rank 13—14 Rank and linear independence 43—47 Rayleigh quotient 104 Reducible matrix 294—295 Regression 26—28 see Regression with standardized explanatory variables 64—65 Regression, best quadratic unbiased estimator 358—360 Regression, F test 387—388 Regression, generalized least squares 141—142 Regression, multiple 55—58 248—249 Regression, principal components 96—98 136—138 163 Regression, ridge 123 Regression, simple linear 50—51 Regression, weighted least squares 65—66 Row space 43 Saddle point 345 Sample correlation matrix 25 Sample correlation matrix, asymptotic covariance matrix of 407—409 Sample covariance matrix 25 Sample covariance matrix, distribution of 402—403 Sample mean 25 Sample mean vector 25 Sample variance 25 Sample variance, distribution 383—384 Sample variance, independent of sample mean 388—389 Schur decomposition 149—153 Separating hyperplane theorem 73—74 Similar matrices 144 Simultaneous confidence intervals 121—122 Simultaneous diagonalization 118 154—157 Singular value decomposition 131—138 Singular value decomposition and system of equations 233—235 Singular values 133 Singular values and eigenvalues 135 Skew-symmetric matrix 4 Spanning set 33 Spectral decomposition 95 98 138 Spectral radius 159 Spectral set 98 Square root of a matrix 16 138—139 Stationary point 345 SubMatrix 11—13 Submatrix, principal 112 subspace 32 Sum of squares for error 27 Sum of squares for treatment 120 Sum of vector spaces 68 Supporting hyperplane theorem 73 Symmetric matrix 4 Taylor formula, first-order 323 325 Taylor formula, kth-order 324 325 Taylor formula, vector function 326 Toeplitz matrix 304—305 Trace 4—5 Trace and eigenvalues 90 Trace, derivative of 332 Transition probabilities 299 TRANSPOSE 3 Transpose product 114—115 142—144 Triangle inequality 18 36 Triangular matrix 2 Two-way classification model 244 259—260 313 Union-intersection procedure 121 367 Unit vector 14 Unitary matrix 18 150 Vandermonde matrix 307—309 Variance 19—20 Variance of quadratic form 391 394 Variance, sample 25 Vec operator 261—265 Vector 2 Vector norm 35 Vector norm, Euclidean norm 36 37 Vector norm, infinity norm 37 Vector norm, max norm 37 Vector norm, sum norm 37 Vector space 32 Vector space, basis of 41—43 Vector space, dimension of 41 Vector space, direct sum 69 Vector space, Euclidean 36 Vector space, intersection 67 Vector space, projection matrix of 52—59 Vector space, sum 68 Vector, normalized 14 Vector, null 2 Vector, orthogonal 14 Vector, orthonormal 14 Vector, unit 14 Wishart distribution 398—409 Wishart distribution and sample covariance matrix 402—403 Wishart distribution, covariance matrix of 401 Wishart distribution, mean of 401
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