Generalized Vectorization, Cross-Products, and Matrix Calculus
Book Details
Format
Hardback or Cased Book
ISBN-10
1107032008
ISBN-13
9781107032002
Publisher
Cambridge University Press
Imprint
Cambridge University Press
Country of Manufacture
US
Country of Publication
GB
Publication Date
Feb 11th, 2013
Print length
275 Pages
Weight
49 grams
Dimensions
23.00 x 15.90 x 2.10 cms
Product Classification:
EconometricsCalculusComputer science
Ksh 18,700.00
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Matrix calculus is an efficient procedure for obtaining many derivatives at once, used in statistics and econometrics. This book studies different concepts of matrix derivatives and a particular brand of mathematics behind matrix calculus, including special matrices whose elements are all zero or one.
This book presents the reader with new operators and matrices that arise in the area of matrix calculus. The properties of these mathematical concepts are investigated and linked with zero-one matrices such as the commutation matrix. Elimination and duplication matrices are revisited and partitioned into submatrices. Studying the properties of these submatrices facilitates achieving new results for the original matrices themselves. Different concepts of matrix derivatives are presented and transformation principles linking these concepts are obtained. One of these concepts is used to derive new matrix calculus results, some involving the new operators and others the derivatives of the operators themselves. The last chapter contains applications of matrix calculus, including optimization, differentiation of log-likelihood functions, iterative interpretations of maximum likelihood estimators and a Lagrangian multiplier test for endogeneity.
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