Format:
1 Online-Ressource (XI, 267 Seiten)
Edition:
First published
ISBN:
9781139424400
Series Statement:
Cambridge books online
Content:
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
Content:
1. Mathematical prerequisites -- 2. Zero-one matrices -- 3. Elimination and duplication matrices -- 4. Matrix calculus -- 5. New matrix calculus results -- 6. Applications
Note:
Title from publisher's bibliographic system (viewed on 24 Feb 2016)
Additional Edition:
ISBN 9781107032002
Additional Edition:
ISBN 9781107448728
Additional Edition:
Erscheint auch als Druck-Ausgabe Turkington, Darrell A., 1947 - Generalized vectorization, cross-products, and matrix calculus Cambridge [u.a.] : Cambridge Univ. Press, 2013 ISBN 9781107032002
Additional Edition:
Print version ISBN 9781107032002
Language:
English
Subjects:
Mathematics
Keywords:
Matrix
;
Vektoranalysis
DOI:
10.1017/CBO9781139424400
URL:
Volltext
(lizenzpflichtig)
