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Graham A. — Kronecker products and matrix calculus: with applications
Graham A. — Kronecker products and matrix calculus: with applications

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Название: Kronecker products and matrix calculus: with applications

Автор: Graham A.

Аннотация:

The book is organised in the following way:
Chapter 1 concentrates on the preliminaries of matrix theory and notation which is found useful throughout the book. In particular, the simple and useful elementary matrix is defined. The vec operator is defined and many useful relations are developed. Chapter 2 introduces and establishes various important properties of the matrix Kronecker product.
Several applications of the Kronecker product are considered in Chapter 3. Chapter 4 introduces Matrix Calculus. Various derivatives of vectors are defined and the chain rule for vector differentiation is established. Rules for obtaining the derivative of a matrix with respect to one of its elements and conversely are discussed. Further developments in Matrix Calculus including derivatives of scalar functions of a matrix with respect to the matrix and matrix differentials are found in Chapter 5.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1981

Количество страниц: 130

Добавлена в каталог: 16.05.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Chain Rule, matrix      88
Chain Rule, vector      54
Characteristic equation      47
Cofactor      57
Column vector      14
Companion form      47
Constrained optimisation      94 96
Decomposition of a matrix      13
Derivative, Kronecker product      70
Derivative, matrix      60 62 64 67 70 75 81
Derivative, scalar function      56 75
Derivative, vector      52
Determinant      27 56
Deviation      94
Direct product      21
Eigenvalues      27 30
Eigenvectors      27 30
Elementary matrix      12 19
Exponential matrix      29 31 42 108
Gradient matrix      56
Jacobian      53 109
Kronecker delta      13
Kronecker delta product      21 23 33 70 85
Kronecker delta sum      30
Langrange multipliers      95
Least squares      94 96 100
Matrix, calculus      51 94
Matrix, companion      47
Matrix, decomposition      13
Matrix, derivative      37 60 62 67 70 75 81 84 88
Matrix, differential      78
Matrix, elementary      12 19
Matrix, exponential      29 31 42 108
Matrix, gradient      56
Matrix, integral      37
Matrix, orthogonal      97
Matrix, permutation      23 28 32
Matrix, product rule      84
Matrix, symmetric      58 95 97
Matrix, transition      42
Maximum likelihood      102
Mixed product rule      24
Multivariable system      45
Multivariate normal      102
Normal equations      95 101
Orthogonal matrix      97
Permutation matrix      23 28 32
Product rule      84 85
Residual      94
Row vector      14
Scalar function      56 75
Spectral decomposition      109
Spur      16
Symmetric matrix      54 57 58 79 95 97
Tensor product      21
Trace      16 30 76
Transformation principle, first      65
Transformation principle, second      74
TRANSPOSE      19
Vec operator      18 25 32 72
Vector, chain rule      54
Vector, column      13
Vector, derivative      52
Vector, normalised      108
Vector, one      12
Vector, row      14
Vector, transposed      12
Vector, unit      11
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