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Graybill F.A. — Matrices with Applications in Statistics
Graybill F.A. — Matrices with Applications in Statistics

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Название: Matrices with Applications in Statistics

Автор: Graybill F.A.

Аннотация:

Part of the Duxbury Classic series, Franklin A. Graybill's MATRICES WITH APPLICATIONS TO STATISTICS focuses primarily on matrices as they relate to areas of multivariate analysis and the linear model. This seminal work is a time tested, authoritative resource for both students and researchers.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2

Год издания: 2001

Количество страниц: 461

Добавлена в каталог: 17.05.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Addition of matrices      4
Analysis of variance      3
Approximate solutions of linear equations      Sec. 7.4
Approximate solutions of linear equations, with constraints      170
Asymptotic equivalence of matrices      101
Band matrices      282 283
Basis      31
Basis, normal orthogonal      34
Basis, orthogonal      34
Centrosymmetric matrix      see Cross-symmetric matrix
Characteristic equations      42
Characteristic polynomial      92
Characteristic roots      42 47 48 98 404
Characteristic roots, bounds on      409
Characteristic roots, of correlation matrix      215
Characteristic roots, of patterned matrices      186 Sec.
Circulants      101 Sec.
Circulants, determinant of      240 241
Circulants, generalized inverse      249
Circulants, inverse      237 242 243
Circulants, product      236 242 244
Circulants, regular      235-241
Circulants, roots      239 246 247
Circulants, sum of      235 242 244
Circulants, symmetric      242 243
Circulants, symmetric regular      241 242
Column space      87 92
Commutation matrix      Sec. 9.3
Commutation matrix , direct product      318
Conditional inverse      Sec. 6.6 117 118 145-148 172-176 180 181 416 417
Conditional inverse, definition      130
Conditional inverse, rank of      134
Conditional inverse, use in linear equations      Sec. 7.3
Conditional inverse, use of Hermite matrices      130
Convergence of matrices      95ff.
Correlation matrix      Sec. 8.7
Cosine, direction      62
Covariance matrix      1 188 189 200 201 335 Sec.
Cross-symmetric matrix      287 288
Cross-symmetric matrix, skew      44
Derivative      Sec. 10.8
Derivative, of a determinant      355 356
Derivative, of a linear function      352
Derivative, of a matrix      353
Derivative, of a quadratic form      352
Derivative, of inverse      357
Derivative, with respect to a matrix      353
Derivative, with respect to a vector      351
Determinant      7 46 413;
Determinant, of circulants      Sec. 8.10
Determinant, of Fourier matrices      272
Determinant, of partitioned matrices      184
Determinant, of patterned matrices      Sec. 8.4
Determinant, of the product of matrices      9
Determinant, of Toeplitz matrices      285 286
Determinant, of Vandermonde matrices      266
Determinant, properties of      8
Diagonal matrices      5
Direct product of matrices      Sec. 8.8
Direct product of matrices, characteristic roots of      226 227
Direct product of matrices, determinant of      224
Direct product of matrices, inverse of      223
Direct product of matrices, of positive definite matrices      227
Direct product of matrices, product of      225
Direct product of matrices, trace of      301
Direct product of matrices, transpose of      221
Direct product of matrices, use with commutation matrices      Sec. 9.3
Direct product of matrices, use with the vector of a matrix      Sec. 9.2
Direct sum of matrices      228 229
Distance      54
Distance, point to line      65
Dominant diagonal matrices      Sec. 8.11
Dominant diagonal matrices, characteristic roots      261
Dominant diagonal matrices, determinants      258
Dominant diagonal matrices, for solving matrix inequations      265
Dominant diagonal matrices, nonsingular matrices      251-256
Dominant diagonal matrices, reducible and irreducible matrices      263
Elementary operations on matrices      11
Equations, set of linear      Chap. 7
Equations, set of linear, c-inverse      Sec. 7.3
Equations, set of linear, g-inverse      Sec. 6.3 Sec.
Equations, set of linear, L-inverse      Sec. 7.6
Euclidean norm      94
Euclidean space      54
Euclidean space, definition      53
Euclidean space, distance      54
Expected value      1 338
Expected value, and direct product      Sec. 10.9
Expected value, of a matrix      339
Expected value, of a quadratic form      340 341 Sjc.
Expected value, of powers of quadratic forms      Sec. 10.9
Expected value, of products of quadratic forms      Sec. 10.9
Expected value, Wishart matrices      Sec. 10.9
Experimental design matrix      194 195 230
Exponential distribution      188
Fourier matrix      Sec. 8.12
Functions of matrices      92 Sec.
Functions of matrices, norm      92
Functions of matrices, polynomial      92
Functions of matrices, sequences of matrices      94ff.
Generalized inverse      Sec. 6.2 172-176 180 181 416 417 440
Generalized inverse, computing      Sec. 6.5 145-148
Generalized inverse, definition      106
Generalized inverse, of circulants      249
Generalized inverse, of diagonal matrix      108
Generalized inverse, of nonsingular matrix      108
Generalized inverse, of some special matrices      Sec. 6.4
Generalized inverse, of symmetric idempotent matrices      111
Generalized inverse, of symmetric matrix      108
Generalized inverse, rank of      108
Generalized inverse, use in best approximate solution of equations      159
Generalized inverse, use in solution of linear equations      Sec. 6.3 152 153
Hadamard matrix      Sec. 8.14
Hermite form of matrices      130 Sec.
Hermite form of matrices, use in computing c-inverse      132
Idempotent matrices      3 Sec. 433 439
Independent vectors      27
Infinite sum of matrices      96ff.
Inverse      198 199 200; General¬ized Least
Inverse positive matrices      Chap. 11
Irreducible matrix      263
Irreducible matrix and dominant diagonal matrix      264
Latin square matrix      194
Leading principal minor      9
Least squares      2
Least squares inverse      Sec. 7.6
Least squares inverse, computation of      169
Least squares inverse, definition of      164
Least squares inverse, use in solution of linear equations      168
Least squares inverse, with constraints      170-176
Least squares, weighted      177
linear combination      27
Linear dependence      27
Linear equations, approximate solution to      Sec. 7.4
Linear equations, best approximate solution      157 159 168
Linear equations, consistency conditions for      150-153
Linear equations, number of solutions      Sec. 7.3
Linear equations, solution of      151-155
Linear equations, two systems      176
Linear equations, use of c-inverse      151-155
Linear equations, use of g-inverse      151-155. 159
Linear equations, use of L-inverse      168
Linear equations, with constraints      170ff.
Linear independence      Sec. 2.4
Linear model      1 2 92
Linear transformations      39
Linear transformations, of vector space      41
Lines, angle between two      59 70
Lines, direction angles of      61
Lines, in $E_{n}$      56
Lines, intersection of      57 70
Lines, parallel      57
Lines, projection of      70
lines, segments      60
Lower triangular matrix      see Triangular matrix
M-matrices      Sec. 11.4
Matrices type 2      198
Matrices, algebra of      4 5
Matrices, characteristic equation of      42
Matrices, characteristic polynomial of      42
Matrices, characteristic roots of      42 47 48
Matrices, characteristic vectors of      42
Matrices, circulants      Sec. 8.10
Matrices, column space of      87
Matrices, congruent      16
Matrices, correlation      Sec. 8.7
Matrices, covariance      335 Sec.
Matrices, diagonal      5
Matrices, direct product of      Sec. 8.8
Matrices, direct sum of      Sec. 8.8
Matrices, elementary      12
Matrices, elementary transformations      11
Matrices, Hermite form of      see Hermite form
Matrices, idempotent      see Idempotent matrices
Matrices, inverse      see Inverse
Matrices, non-negative      Sec. 12.1
Matrices, null space      87
Matrices, orthogonal      see Orthogonal
Matrices, P-matrices      Sec. 11.2
Matrices, partitioned      Sec. 8.2
Matrices, positive definite      208 Sec. 438;
Matrices, positive semidefinite      Sec. 12.2
Matrices, rank      10
Matrices, reducible      263
Matrices, similar      45
Matrices, skew symmetric      415
Matrices, symmetric      7 47 48
Matrices, trace of      see Trace
Matrices, transformation of random variables      Sec. 10.2
Matrices, transpose of      6
Matrices, triangular      see Triangular
Matrices, tripotent matrices      see Tripotent matrices
Matrices, with non-positive off-diagonal elements      see Z-matrices
Matrices, with positive elements      374
Matrices, with positive principal minors      see P-matrices M-matrices
Matrices, Z-matrices      Sec. 11.3
Maximum likelihood      2
Minimum polynomial      92
Moment generating function      350
Moments of normal distribution      Sec. 8.4
Multinomial distribution      189
Multivariate normal distribution      Sec. 10.3
n-dimensional geometry      53
n-dimensional geometry, equation of a line      54
n-dimensional geometry, equation of a plane      65
n-dimensional vector space      53
n-tuples, ordered      23
n-tuples, space of      24
Non-negative matrices      Sec. 12.2
Norm      93ff.
Normal distribution      Sec. 10.3
Normal distribution, covariance      Sec. 10.3 Sec.
Normal distribution, mean      Sec. 10.4
Normal distribution, variance      Sec. 10.4
Normal equations      161
Null matrix      5
Null space      87
Order statistics      188
Orthogonal complement of a subspace      83
Orthogonal matrix      18 48
Orthogonal projections      see Projections
Orthogonal set of vectors      35 47
Orthogonal transformations      19
P-matrices      Sec. 11.2 Sec.
Parameter space      91
Partitioned matrix      Sec. 8.5
Partitioned matrix, characteristic roots      Sec. 8.5
Partitioned matrix, determinant of      184 231
Partitioned matrix, generalized inverse of      Sec. 7.6
Partitioned matrix, inverse of      184
Patterned matrices      Sec. 8.3 Sec.
Patterned matrices, conditional inverse of      449
Patterned matrices, determinant of      184 Sec.
Patterned matrices, generalized inverse of      Sec. 7.6
Patterned matrices, inverse of      184 Sec.
Permutation matrices      Sec. 8.13
Planes      65 69
Positive definite      Sec. 12.2
Positive semidefinite      Sec. 12.2
Projections      70 85 Sec.
Quadratic form      14 273 Sec.
Quadratic form, derivative of      352
Quadratic form, expected value      Sec. 12.2
Quadratic form, index      16
Quadratic form, matrix of      15
Quadratic form, non-negative      Sec. 12.2
Quadratic form, positive definite      Sec. 12.2 17
Quadratic form, positive semidefinite      17 Sec.
Quadratic form, real symmetric      16
Quadratic function      15
Random variables      Sec. 10.2
Random variables, expected value      338 339 Sec.
Random variables, moments of      Sec. 10.2
Random variables, transformations      Sec. 10.2
Range space      87
Rank      Sec. 1.6; see under each type of matrix
Rank of a matrix      18
Rank of conditional inverse      134
Rank of direct product      227
Rank of the generalized inverse      109
Rectangular distribution      100
Reducible matrix      263
Sequence of matrices      95ff.
Sequence of matrices, limit of      95
Skew-symmetric matrix      444
Space      87 92 column
Spectral norm      94
Statistical applications      Sec. 7.5 Sec.
Statistical applications, use of generalized inverse      162 163
Subspaces      25
Subspaces, intersection of      79
Subspaces, orthogonal      83
Subspaces, sum of      80
Symmetric matrix      see Matrices symmetric
Systems of linear equations      Sec. 6.3
Systems of linear equations, augmented matrix of      151
Systems of linear equations, best approximate solutions      Sec. 7.4
Systems of linear equations, consistent      149
Systems of linear equations, least squares solution      Sec. 7.4
Systems of linear equations, solution of      152-156
Toeplitz matrix      101 Sec.
Trace of a matrix      Sec. 9.1
Trace of a matrix, of non-negative matrices      397 398 399
TRANSPOSE      Sec. 1.4
Triangular matrix      46 Sec.
Triangular matrix, characteristic roots of      210 212
Triangular matrix, determinant of      210
Triangular matrix, factoring into      207 208 209 210 212
Triangular matrix, inverse of      209
Triangular matrix, product of      212 213
Triangular matrix, reduction to      211 212 213
Tripotent matrices      Sec. 12.4 438
Vandermonde matrix      Sec. 8.12
Variance      1
Variance of quadratic forms      Sec. 10.9
Vector addition      24
Vector components      23
Vector direction      61
Vector equality      24
Vector of a matrix      Sec. 9.2 316 317
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