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

By:

Turkington, Darrell A [author.]

Contributor(s):

Cambridge eBooks

Publisher: Cambridge : Cambridge University Press, 2013Description: 1 online resource (xi, 267 pages) : digital, PDF file(s)Content type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9781139424400 (ebook)

Other title:

Generalized Vectorization, Cross-Products, & Matrix Calculus

Subject(s):

Genre/Form:

Electronic books.

Additional physical formats: Print version: : No titleDDC classification:

515/.63 23

LOC classification:

QA188 .T8645 2013

Online resources:

Click here to access online

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.

Item type:

eBooks

Average rating: 0.0 (0 votes)

Holdings ( 0 )
Title notes ( 3 )

No physical items for this record

Title from publisher's bibliographic system (viewed on 24 Feb 2016).

1. Mathematical prerequisites -- 2. Zero-one matrices -- 3. Elimination and duplication matrices -- 4. Matrix calculus -- 5. New matrix calculus results -- 6. Applications.

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.