02975cam a2200265 i 4500008004100000020001800041040000800059050002300067100003600090245012600126260005400252300001100306505020000317505001700517518001500534520016000549520170600709650001402415650002802429650004902457900001402506942001302520999001902533952015702552120531s2013    enk      b    001 0 eng    a9781107032002  aSDU00aQA188bT939 G 20131 aTurkington, Darrell A.,921095710aGeneralized vectorization, cross-products, and matrix calculus /cDarrell A. Turkington, University of Western Australia.  aCambridge : bCambridge University Press, c2013.  a267 p.8 aMachine generated contents note: 1. Mathematical prerequisites; 2. Zero-one matrices; 3. Elimination and duplication matrices; 4. Matrix calculus; 5. New matrix calculus results; 6. Applications.8 aHKBU library  aYT2025 M10  a"This book studies the mathematics behind matrix calculus, and the final chapter looks at applications of matrix calculus in statistics and econometrics"--  a"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"-- 0aMatrices. 0aVector analysis.928332 7aBUSINESS & ECONOMICS / Econometrics.9202671  a= C.1 SDU  cGBE2lcc  c109397d109397  00102lcc406QA0188 T939 G2013708CGB9283657aSDUbSDUcGEN3d2025-10-01e2oQA188 T939 G 2013p1000385327r2025-10-01 00:00:00tC.1w2025-10-01yGBE