Generalized vectorization, cross-products, and matrix calculus

著者

• Turkington, Darrell A.

書誌事項

Generalized vectorization, cross-products, and matrix calculus

Darrell A. Turkington

Cambridge University Press, 2013

注記

Includes bibliographical references (p. 257-258) and index

内容説明・目次

内容説明

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.

目次

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

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BB12183510
• ISBN:
  • 9781107032002
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cambridge
• ページ数/冊数: xi, 267 p.
• 大きさ: 24 cm
• 分類:
  • DC23 : 515.63
• 件名:
  • LCSH : Matrices
  • LCSH : Vector analysis