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Generalized Vectorization, Cross-Products, and Matrix Calculus

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Title: Generalized Vectorization, Cross-Products, and Matrix Calculus
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.
Authors: Darrell A. Turkington
Resource Type: eBook.
Subjects: Matrices, Vector analysis
Categories: MATHEMATICS / Vector Analysis
Database: eBook Collection (EBSCOhost)
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Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 508300
RelevancyScore: 1051
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1050.81640625
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  Data: 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.
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  Data: <searchLink fieldCode="AR" term="%22Darrell+A%2E+Turkington%22">Darrell A. Turkington</searchLink>
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RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 515.63
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Matrices
        Type: general
      – SubjectFull: Vector analysis
        Type: general
    Titles:
      – TitleFull: Generalized Vectorization, Cross-Products, and Matrix Calculus
        Type: main
  BibRelationships:
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      – PersonEntity:
          Name:
            NameFull: Darrell A. Turkington
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          Name:
            NameFull: Darrell A. Turkington
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2013
            – D: 04
              M: 02
              Type: profile
              Y: 2014
          Identifiers:
            – Type: isbn-print
              Value: 9781107032002
            – Type: isbn-electronic
              Value: 9781139626064
          Titles:
            – TitleFull: Generalized Vectorization, Cross-Products, and Matrix Calculus
              Type: main
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