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Generalized vectorization, cross-products, and matrix calculus / Darrell A. Turkington

Author
Turkington, Darrell A.
Additional Titles
Generalized Vectorization, Cross-Products, & Matrix Calculus
Published
Cambridge : Cambridge University Press, 2013.
Physical Description
1 online resource (xi, 267 pages) : digital, PDF file(s).
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Contents
1. Mathematical prerequisites -- 2. Zero-one matrices -- 3. Elimination and duplication matrices -- 4. Matrix calculus -- 5. New matrix calculus results -- 6. Applications.
Summary
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.
Subject(s)
ISBN
9781139424400 (ebook)
9781107032002 (hardback)
9781107448728 (paperback)
Note
Title from publisher's bibliographic system (viewed on 24 Feb 2016).
View MARC record | catkey: 34849407