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

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

Label
Generalized vectorization, cross-products, and matrix calculus
Title
Generalized vectorization, cross-products, and matrix calculus
Statement of responsibility
Darrell A. Turkington
Creator
Subject
Language
eng
Summary
  • "This book studies the mathematics behind matrix calculus, and the final chapter looks at applications of matrix calculus in statistics and econometrics"--
  • "In this chapter we consider elements of matrix algebra, knowledge of which is essential for our future work. This body of mathematics centres around the concepts of Kronecker products and vecs of a matrix. From the elements of a matrix and a matrix the Kronecker product forms a new matrix. The vec operator forms a column vector from the elements of a given matrix by stacking its columns one underneath the other. Several new operators considered in this chapter are derived from these basic operators. The operator which I call the cross product operator takes the sum of Kronecker products formed from submatrices of two given matrices. The rvec operator forms a row vector by stacking the rows of a given matrix alongside each other. The generalized vec operator forms a new matrix from a given matrix by stacking a certain number of its columns, taken as a block, under each other, and the generalized rvec operator forms a new matrix by stacking a certain number of rows, again taken as a block, alongside each other. It is well known that Kronecker products and vecs are intimately connected but this connection also holds for rvec and generalized operators as well. The cross sum operator, as far as I know, is being introduced by this book. As such, I will present several theorems designed to investigate the properties of this operator. The approach I have taken in this book is to list, without proof, well-known properties of the mathematical operator or concept in hand. If, however, I am presenting the properties of a new operator or concept, if I am presenting a property in a different light, or finally if I have something new to say about the concept, then I will give a proof"--
Assigning source
  • Provided by publisher
  • Provided by publisher
Cataloging source
DLC
http://library.link/vocab/creatorName
Turkington, Darrell A
Illustrations
illustrations
Index
index present
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/subjectName
  • Matrices
  • Vector analysis
Label
Generalized vectorization, cross-products, and matrix calculus, Darrell A. Turkington
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier.
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
1. Mathematical prerequisites; 2. Zero-one matrices; 3. Elimination and duplication matrices; 4. Matrix calculus; 5. New matrix calculus results; 6. Applications
Control code
FIEb17504958
Dimensions
24 cm.
Extent
xi, 267 pages
Isbn
9781107032002
Media category
unmediated
Media MARC source
rdamedia.
Media type code
  • n
Other physical details
illustrations
System control number
(OCoLC)800444338
Label
Generalized vectorization, cross-products, and matrix calculus, Darrell A. Turkington
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier.
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
1. Mathematical prerequisites; 2. Zero-one matrices; 3. Elimination and duplication matrices; 4. Matrix calculus; 5. New matrix calculus results; 6. Applications
Control code
FIEb17504958
Dimensions
24 cm.
Extent
xi, 267 pages
Isbn
9781107032002
Media category
unmediated
Media MARC source
rdamedia.
Media type code
  • n
Other physical details
illustrations
System control number
(OCoLC)800444338

Library Locations

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