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  3. Generalized Vectorization, Cross-Products, and Matrix Calculus
  • Cited by 14
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    • Publisher:
      Cambridge University Press
      Publication date:
      05 February 2013
      11 February 2013
      ISBN:
      9781139424400
      9781107032002
      9781107448728
      DOI:
      https://doi.org/10.1017/CBO9781139424400
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.49kg, 275 Pages
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.43kg, 280 Pages
      • Subjects:
      Economics, Mathematics, Computational Science, Econometrics and Mathematical Methods
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    • Selected: Digital
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    Subjects:
    Economics, Mathematics, Computational Science, Econometrics and Mathematical Methods
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    Book description

    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.

    Reviews

    ‘A very neat treatment of matrix calculus. There is no doubt that the new operators and matrices presented in the book will see their applications in many areas of econometrics.’

    Yong Bao - Purdue University

    'This book is very clearly written in a text style that conveys what needs to be said with no superfluous discussion. It represents a substantial contribution to our understanding of a difficult area. It is a beautiful book, and destined to become a classic.’

    Ross Maller - Australian National University

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