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Searle S.R. — Matrix algebra useful for statistics
Searle S.R. — Matrix algebra useful for statistics

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Название: Matrix algebra useful for statistics

Автор: Searle S.R.

Аннотация:

An easy to understand guide to matrix algebra and its uses in statistical analysis. Presents material in an explanatory style instead of the formal theorem-proof format; the only background necessary is high school algebra. The self-contained text includes numerous applied illustrations, numerical examples, and exercises.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1982

Количество страниц: 464

Добавлена в каталог: 17.03.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Addition      28
Adjoint matrix      128
Adjugate matrix      128
Adjugate matrix, a$\mathbf{I}$ + $b{\mathbf{J}$ 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$\mathbf{I} + $b$\mathbf{J}$      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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