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| Searle S.R. — Matrix algebra useful for statistics |
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| Предметный указатель |
Addition 28
Adjoint matrix 128
Adjugate matrix 128
Adjugate matrix, a +  matrix 322
Adjugate matrix, inverse 132
Aitken equations 357
Aitken’s integral 340
Associative laws of algebra 50
Augmented matrix 232
Basis 179
Bilinear form 76
Calculus results 334
Canonical form 184
Canonical form, congruent 201
Canonical form, equivalent 190
Canonical form, orthogonal similar 291
Canonical form, similar 283
Canonical form, summary 323
Cauchy — Schwartz inequality 59
Cayley — Hamilton theorem 314
Centering matrix 67 350
Characteristic equation 274
Characteristic equation, factoring 298
Characteristic root (and vector) 274
Chi-square distribution 354
Cofactor 93 125
column 3
Column, operations 185
Column, space 180
Column, vector 15
Comformable, for addition 29
Comformable, for addition for multiplication 38
Comformable, for addition for subtraction 31
Commutative laws of algebra 51
Complementary minor 108
Complementary minor, principal 108
Complex conjugate 341
Computing inverses 139
Contrasts among means 358
Correlation matrix 348
Cramer’s Rule 118
Cumulants, of normal 356
Data matrix 349
Decompositions 323
Deficient (defective) matrix 284
Determinant 84 90
Determinant, expansion 87
Determinant, geometry 117
Determinant, order 85
Determinant, partitioned matrix 258
Determinant, product 98
Determinant, transpose 92
Diagonability theorem 305
Diagonal 13
Diagonal expansion 106
Diagonal form, symmetric matrix 201
Diagonal off 13
Diagonal, clciticui 13
Diagonal, matrix 13 132
Diagonal, non 13
Diagonal, product with 43
Diagonal, secondary 88
Diagonal, sub 13
Differential operators, vector of 327
Differentiation, determinant 336
Differentiation, determinant, 433
Differentiation, determinant, inverse 335
Differentiation, determinant, trace 336
Dimension, of matrix 13
Dimension, of matrix of space 179
Direct product 265
Direct product, left 266
Direct product, right 266
Direct sum 263
Dispersion matrix 347
Distributive laws of algebra 51
dot notation 11
Doubly stochastic 83
Effective inverse 216
Eigen root 272
Eigen root, multiple 280
Eigenvalue 272
Eigenvector 272
Eigenvector, regular 284
Element 4 12
Element off-diagonal 13
Element, complex numbers 341
Element, diagonal 13
Element, leading 13
Element, non-diagonal 13
Element, sub-diagonal 13
Elementary operator matrix 100
Elementary operators 184
Elementary operators, inverses 185
Elementary operators, products 186
Elementary operators, rank of matrix 186
Elementary operators, transposes 185
Elementary row operations 99 (see also “Row operations”)
Elementary vector 65
Equality 31
Equations, linear 227
Equivalent matrices 187
Factorization 175
Full column rank 172
Full rank 172
Full rank, factorization 175 194 205
Full rank, non-negative definite matrix 206
Full row rank 171 208
Functions of matrices 325
G-inverse 216
Generalized inverse 212
Generalized inverse, normalized 216
Generalized inverse, other names 216
Generalized inverse, partitioned matrix 261
Generalized inverse, reflexive 216
Generalized inverse, weak 216
Givens matrix (transformation) 72
Graph theory 46
Hadamard inequality 260
Hadamard product 49
Helmert matrix 71
Hermitian matrix 341
Hessian matrix 341
Householder matrix 72
Idempotent matrix 68 133
Idempotent matrix, summary 320
Identity matrix 44
Identity matrix, products equal to 123
Ill-conditioned 146
Illustrations 16
Illustrations of rabbits 296
Illustrations, age distributions 133
Illustrations, ancestor records 258
Illustrations, Bernadelli’s beetles 275 287
Illustrations, corporate income 30
Illustrations, correlation matrix 260
Illustrations, correlations 60
Illustrations, games against nature 56
Illustrations, gene effects 158
Illustrations, genetics 120
Illustrations, geometry 117
Illustrations, graph theory 46
Illustrations, inbreeding 35 159
Illustrations, input-output analysis 134
Illustrations, larvae counts 119
Illustrations, least squares 330
Illustrations, linear difference equations 288
Illustrations, linear models 392
Illustrations, linear programming 41
Illustrations, lunch servings 28
| Illustrations, Markov chain 288
Illustrations, Markov chain, genetics 57 286
Illustrations, Markov chain, taxicab 14 41 46 50
Illustrations, maximum likelihood 341
Illustrations, mean and variance 67
Illustrations, prices and costs 32
Illustrations, pulmonary tuberculosis 138
Illustrations, random mating 266
Illustrations, regression 363
Illustrations, selection index 331
Illustrations, statistics 346 (see also “Statistics”)
Illustrations, sterile cultures 3
Illustrations, sum of squares 77
Illustrations, transition probabilities 49
Illustrations, transition probability matrix 68
Illustrations, transportation problems 115
Inner product 33
Input-output analysis 134
Invariance, solutions to equations 242
Inverse matrix 119
Inverse matrix, a b 132
Inverse matrix, algebraic simplifications 136
Inverse matrix, existence of 129
Inverse matrix, left 147
Inverse matrix, order 2 131
Inverse matrix, orthogonal 132
Inverse matrix, partitioned matrix 260
Inverse matrix, right 147
Jacobian 338
Jacobian matrix 338
Kronecker product 265 334
Lambda root 274
Laplace expansion 109
Latent root (and vector) 274
Laws of algebra, associative 50
Laws of algebra, associative, commutative 51
Laws of algebra, associative, distributive 51
Leading element 13
Least squares, equations 251 357
Least squares, equations, generalized 357
Least squares, equations, ordinary 357
Left direct product 266
Left inverse 147
Lin 162
Linear combination of vectors 155
Linear dependence 159
Linear difference equations 288
Linear equations 227
Linear independence 159
Linear models 392
Linear programming 41
Linear transformation 157
Linearly dependent vectors 159 160
Linearly dependent vectors, inverse matrices 164
Linearly dependent vectors, partitioned matrices 163
Linearly dependent vectors, zero determinants 164
Linearly independent vectors 160 166
Linearly independent vectors, linear combinations of 167
Manifold 180
Markov chain see “Illustrations”
Matrix 3 12
Matrix algebra 4
Matrix algebra, contrasts with scalars 52
Matrix algebra, uses 2
Matrix of dominances 58
Matrix of functions 325
Matrix, 24
Matrix, adjoint 128
Matrix, adjugate 128
Matrix, augmented 232
Matrix, centering 67 350
Matrix, correlation 348
Matrix, data 349
Matrix, defective 284
Matrix, deficient 284
Matrix, diagonable 284
Matrix, diagonal 13
Matrix, dispersion 347
Matrix, doubly stochastic 83
Matrix, effective inverse 216
Matrix, elementary operator 100
Matrix, elements all equal 65
Matrix, full column rank 208
Matrix, full rank 208
Matrix, full row rank 208
Matrix, g-inverse 216
Matrix, generalized inverse 212
Matrix, Givens 72
Matrix, Helmert 71
Matrix, hermitian 341
Matrix, Hessian 341
Matrix, Householder 72
Matrix, idempotent 68 320
Matrix, identity 44
Matrix, ill-conditioned 146
Matrix, inverse 119
Matrix, Jacobian 339
Matrix, left inverse 147
Matrix, lower triangular 14
Matrix, Moore — Penrose inverse 212
Matrix, nilpotent 69 321
Matrix, non-negative definite (n.n.d.) 77 309
Matrix, non-singular 130
Matrix, normalized generalized inverse 216
Matrix, null 31
Matrix, orthogonal 69 320
Matrix, P-inverse 216
Matrix, pay-off 56
Matrix, permutation 173
Matrix, positive (semi) definite 77
Matrix, powers of 46
Matrix, real 4
Matrix, reciprocal 122
Matrix, reflexive generalized inverse 216
Matrix, regret 56
Matrix, regular 284
Matrix, right inverse 147
Matrix, scalar 44
Matrix, Schur complement 261
Matrix, singular 130
Matrix, skew symmetric 65
Matrix, square 13
Matrix, sub 25
Matrix, sums of squares and products 349
Matrix, symmetric 60
Matrix, transition probability 14 68
Matrix, transpose 22
Matrix, triangular 14
Matrix, unipotent 69 321
Matrix, unit 44
Matrix, unitary 342
Matrix, upper triangular 14
Matrix, variance-covariance 347
Matrix, vec-permutation 334
Matrix, weak generalized inverse 216
Matrix, Wishart 352
Matrix, zero 32
minimax 56
Minor 86 106
Minor, complementary 109
Minor, complementary, principal 108
Minor, principal 107
Minor, signed 93
Moore-Penrose inverse 212
Multiple (eigen) root 280
Multiplication 32
Multiplication of matrices 36
Multiplication, inner product 33
Multiplication, matrix-vector 32
Multiplication, on left 39
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