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| Авторизация |
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| Поиск по указателям |
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| Searle S.R. — Matrix algebra useful for statistics |
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| Предметный указатель |
Multiplication, on right 39
Multiplication, post 39
Multiplication, pre 39
Multiplication, scalar 29
Multiplicity 281
Nilpotent matrix 69 321
Non-diagonal 13
Non-linear equations 326
Non-negative definite 77 309
Non-negative definite, congruent canonical form 206
Non-negative definite, generalized inverse 220
Non-negative definite, summary 322
Non-singular matrix 130
Norm 69
Normal distribution 352
Normal distribution, cumulants of 356
Normalized generalized inverse 216
Normalized vector 70
Null, matrix 32 43
Null, matrix, space 180
Null, matrix, vector 161
Nullity 180
Off-diagonal 13
Order, of determinant 85
Order, of determinant of matrix 13
Orthogonal 69
Orthogonal complement 249
Orthogonal, eigenvectors 290
Orthogonal, inverse 132
Orthogonal, Matrix 69 320
Orthogonal, partitioned matrix 257
Orthogonal, similarity 291
Orthogonal, solutions of equations 246
Orthogonal, vector space 248
Orthogonal, vectors 70
Orthonormal vectors 70
P-inverse 216
Partitioned matrix 24 163 257
Partitioned matrix, determinant 258
Partitioned matrix, generalized inverse 261
Partitioned matrix, into vectors 26
Partitioned matrix, inverse 260
Partitioned matrix, product of 48
Partitioned matrix, transpose 26
Pay-off matrix 56
Permutation matrix 173
Positive (semi) definite 77
Principal minor 107
PRODUCT 32
Product notation 11
Product of partitioned matrices 48
Product of two matrices 36
Product with diagonal matrix 43
Product with null matrix 43
Product with scalar 42
Product, existence 38
Product, Hadamard 49
Product, inner 33
Product, matrix-vector 33
Product, outer 40
Product, trace of 45
Product, transpose of 44
Pseudo inverse 216
Quadratic form 73 329
Quadratic form, chi-square distribution 354
Quadratic form, differentiation 329
Quadratic form, distribution 356
Quadratic form, expected value 355
Quadratic form, independence 356
Quadratic form, positive definite 77
Quadratic form, sum of squares 206
RANGE 180
Rank 155 171
Rank, elementary operators 186
Rank, inverse matrices 172
Rank, non-zero eigenvalues 292 305
Rank, product matrix 196
Reciprocal matrix 122
Reflexive generalized inverse 216
Regression 363
Right direct product 266
Right inverse 147
Row 3
Row echelon form 188
Row operations 99 142 184
Row sum 14 116
Row vector 15
scalar 16
Scalar, matrix 44
Scalar, multiplication 29
Schur complement 261
Secondary diagonat 88
Similar canonical form 283
Simple (eigen) root 280
Singular matrix 130
Singular value decomposition 316
Singular values 317
Skew symmetric matrix 65
Solution space 249
Spanning set 179
Spectral decomposition 308
| Square matrix 13
State (probability) vector 41 68
State (probability) vector, steady 59
Statistics 346
Statistics, Aitken equations 357
Statistics, Aitken’s integral 340
Statistics, chi-square distribution 354
Statistics, contrasts among means 358
Statistics, correlation matrix 348
Statistics, cumulants, of normal 356
Statistics, data matrix 349
Statistics, dispersion matrix 347
Statistics, distribution of quadratic forms 356
Statistics, least squares 251 357
Statistics, linear models 392
Statistics, Markov chain 288 (see also “Illustrations”)
Statistics, mean 67
Statistics, normal distribution 352
Statistics, regression 363
Statistics, sum of squares 77
Statistics, sums of squares and products matrix 349
Statistics, variance 67
Statistics, variance-covariance matrix 347
Statistics, Wishart matrix 352
Steady state vector 59
Sub-diagonal 13
Sub-matrix 25
Subscripts 5
Subscripts, elements of matrix 5
Subtraction 30
Summation notation 6
Summation notation, dot subscript 11
Summing vector 66
Sums of squares and products matrix 349
Symmetric matrix 60 308
Symmetric matrix of quadratic form 75
Symmetric matrix,  and  61
Symmetric matrix, canonical form 201
Symmetric matrix, congruent form 201
Symmetric matrix, diagonal form 201
Symmetric matrix, eigenvalues 290
Symmetric matrix, eigenvectors 290
Symmetric matrix, generalized inverse 220
Symmetric matrix, inverse 130
Symmetric matrix, product of vectors 63
Symmetric matrix, products 61
Symmetric matrix, row and column operations 199
Symmetric matrix, skew symmetric 65
Symmetric matrix, spectral decomposition 308
Symmetric matrix, sum of outer products 64
Trace 27
Trace of product 45
Trace of sum 29
Transformation, linear 157
Transition probabilities 14
TRANSPOSE 22
Transpose of product 44
Transpose of sum 29
Triangular matrix 14
Triangular matrix, lower 14
Triangular matrix, reduction to 96
Triangular matrix, upper 14
Unipotent matrix 69 321
Unit matrix 44
Unit vector 70
Unitary matrix 342
Upper triangular matrix 14
Variance-covariance matrix 347
Vec (and vech) operators 332
Vec-permutation matrix 334
Vectors 15
Vectors of ones 66
Vectors, age distribution 272
Vectors, characteristic 274
Vectors, column 15
Vectors, differential operators 327
Vectors, eigen 274
Vectors, elementary 65
Vectors, latent 274
Vectors, linear combinations 155
Vectors, linearly dependent 159
Vectors, linearly independent 160
Vectors, norm of 69
Vectors, normalized 70
Vectors, null 161
Vectors, orthogonal 70
Vectors, orthonormal 70
Vectors, products of 63
Vectors, row 15
Vectors, space 177
Vectors, space, orthogonal 248
Vectors, state 68
Vectors, state, probability 41
Vectors, steady state probabilities 288
Vectors, subspace 180
Vectors, summing 66
Vectors, unit 70
Weak generalized inverse 216
Wishart matrix 352
Zehfuss product 265
Zero matrix 32
“One” vector 66
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