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001    ocn821617824 
003    OCoLC 
005    20190405013903.8 
006    m     o  d         
007    cr cnu---unuuu 
008    121217s2013    enka    ob    001 0 eng d 
019    828302639|a837646008|a848654914|a874420044|a892431441 
020    9781139616768|q(electronic book) 
020    1139616765|q(electronic book) 
020    9781139626064|q(electronic book) 
020    113962606X|q(electronic book) 
020    9781139424400|q(electronic book) 
020    1139424408|q(electronic book) 
020    9781139613040|q(electronic book) 
020    1139613049|q(electronic book) 
020    |z9781107032002 
020    |z1107032008 
020    |z9781283870696 
020    |z128387069X 
035    (OCoLC)821617824|z(OCoLC)828302639|z(OCoLC)837646008
       |z(OCoLC)848654914|z(OCoLC)874420044|z(OCoLC)892431441 
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049    RIDW 
050  4 QA188|b.T8645 2012eb 
072  7 MAT|x033000|2bisacsh 
082 04 515/.63|223 
084    BUS021000|2bisacsh 
090    QA188|b.T8645 2012eb 
100 1  Turkington, Darrell A.,|0https://id.loc.gov/authorities/
       names/n83311696|eauthor. 
245 10 Generalized vectorization, cross-products, and matrix 
       calculus /|cDarrell A. Turkington. 
264  1 Cambridge :|bCambridge University Press,|c2013. 
300    1 online resource (xi, 267 pages) :|billustrations 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
340    |gpolychrome|2rdacc 
347    text file|2rdaft 
504    Includes bibliographical references and index. 
505 0  1. Mathematical prerequisites -- 2. Zero-one matrices -- 
       3. Elimination and duplication matrices -- 4. Matrix 
       calculus -- 5. New matrix calculus results -- 6. 
       Applications. 
505 0  Preface; one Mathematical Prerequisites; 1.1 Introduction;
       1.2 Kronecker Products; 1.3 Cross-Product of Matrices; 1.4
       Vecs, Rvecs, Generalized Vecs, and Rvecs; 1.4.1 Basic 
       Operators; 1.4.2 Vecs, Rvecs, and the Cross-Product 
       Operator; 1.4.3 Related Operators: Vech and; 1.4.4 
       Generalized Vecs and Generalized Rvecs; 1.4.5 Generalized 
       Vec Operators and the Cross-Product Operator; two Zero-One
       Matrices; 2.1 Introduction; 2.2 Selection Matrices and 
       Permutation Matrices; 2.3 The Elementary Matrix; 2.4 The 
       Commutation Matrix; 2.4.1 Commutation Matrices, Kronecker 
       Products, and Vecs. 
505 8  2.4.2 Commutation Matrices and Cross-Products2.5 
       Generalized Vecs and Rvecs of the Commutation Matrix; 
       2.5.1 Deriving Results for Generalized Vecs and Rvecs of 
       the Commutation Matrix; 2.5.2 Generalized Vecs and Rvecs 
       of the Commutation Matrix and Cross-Products; 2.5.3; 2.5.4
       The Matrix; 2.6 The Matrix; 2.7 Twining Matrices; 2.7.1 
       Introduction; 2.7.2 Definition and Explicit Expressions 
       for a Twining Matrix; 2.7.3 Twining Matrix and the 
       Commutation Matrix; 2.7.4 Properties of the Twining Matrix
       .; 2.7.5 Some Special Cases; 2.7.6 Kronecker Products and 
       Twining Matrices; 2.7.7 Generalizations. 
505 8  A More General Definition of a Twining Matrix2.7.8 
       Intertwining Columns of Matrices; Three Elimination and 
       Duplication Matrices; 3.1 Introduction; 3.2 Elimination 
       Matrices; 3.2.1 The Elimination Matrix; 3.2.2 The 
       Elimination Matrix; 3.2.3 The Elimination Matrices and; 
       3.2.4 The Elimination Matrices; 3.3 Duplication Matrices; 
       3.3.1 The Duplication Matrix; 3.3.2 The Elimination Matrix
       and the Duplication Matrix; 3.3.3 The Duplication Matrix; 
       Four Matrix Calculus; 4.1 Introduction; 4.2 Different 
       Concepts of a Derivative of a Matrix with Respect to 
       Another Matrix. 
505 8  4.3 The Commutation Matrix and the Concepts of Matrix 
       Derivatives4.4 Relationships Between the Different 
       Concepts; 4.5 Transformation Principles Between the 
       Concepts; 4.5.1 Concept 1 and Concept 2; 4.5.2 Concept 1 
       and Concept 3; 4.5.3 Concept 2 and Concept 3; 4.6 
       Transformation Principle One; 4.7 Transformation Principle
       Two; 4.8 Recursive Derivatives; Five New Matrix Calculus 
       Results; 5.1 Introduction; 5.2 Concept of a Matrix 
       Derivative Used; 5.3 Some Basic Rules of Matrix Calculus; 
       5.4 Matrix Calculus Results Involving Generalized Rvecs or
       Cross-Products. 
505 8  5.5 Matrix Derivatives of Generalized Vecs and Rvecs5.5.1 
       Introduction; 5.5.2 Large X; Results for Generalized 
       rvecs; Results for Generalized vecs; 5.5.3 Small X; 
       Results for Generalized rvecs; Result for Generalized 
       vecs; 5.6 Matrix Derivatives of Cross-Products; 5.6.1 
       Basic Cross-Products; 5.6.2 Cross-Products Involving; 
       5.6.3 Cross-Products Involving; 5.6.4 The Cross-Product; 
       5.6.5 The Cross-Product; 5.6.6 The Cross-Product; 5.7 
       Results with Reference to; 5.7.1 Introduction; 5.7.2 
       Simple Theorems Involving; 5.7.3 Theorems Concerning 
       Derivatives Involving VecA, VechA, and. 
520    "This book studies the mathematics behind matrix calculus,
       and the final chapter looks at applications of matrix 
       calculus in statistics and econometrics"--|cProvided by 
       publisher. 
520    "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"--
       |cProvided by publisher. 
588 0  Print version record. 
590    eBooks on EBSCOhost|bEBSCO eBook Subscription Academic 
       Collection - North America 
650  0 Matrices.|0https://id.loc.gov/authorities/subjects/
       sh85082210 
650  0 Vector analysis.|0https://id.loc.gov/authorities/subjects/
       sh85142449 
650  7 Matrices.|2fast|0https://id.worldcat.org/fast/1012399 
650  7 Vector analysis.|2fast|0https://id.worldcat.org/fast/
       1164651 
655  4 Electronic books. 
655  7 Electronic books.|2lcgft 
776 08 |iPrint version:|aTurkington, Darrell A.|tGeneralized 
       vectorization, cross-products, and matrix calculus.
       |dCambridge : Cambridge University Press, 2013
       |z9781107032002|w(DLC)  2012022017|w(OCoLC)800444338 
856 40 |uhttps://rider.idm.oclc.org/login?url=http://
       search.ebscohost.com/login.aspx?direct=true&scope=site&
       db=nlebk&AN=508300|zOnline eBook via EBSCO. Access 
       restricted to current Rider University students, faculty, 
       and staff. 
856 42 |3Instructions for reading/downloading the EBSCO version 
       of this eBook|uhttp://guides.rider.edu/ebooks/ebsco 
901    MARCIVE 20231220 
948    |d20190507|cEBSCO|tEBSCOebooksacademic NEW 4-5-19 7552
       |lridw 
994    92|bRID