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 Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум Авторизация Поиск по указателям     Searle S.R. — Matrix algebra useful for statistics Обсудите книгу на научном форуме Нашли опечатку?Выделите ее мышкой и нажмите Ctrl+Enter 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: 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 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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