Fernando De la Torre <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>... > Hi all, > > I want to make the matrix derivative of an expression like: > > min over B of sum_i A_i B(B^TW_iB^T)^-1 B^TA_i subject to > B^TB=Identity. > > where B^T denotes transpose of B and it is an arbitrary matrix. > > Do you know any good reference book which show how to make derivatives > w.r.t. the pseudo-inverse or in general > any good reference for matrix derivatives. Or any goo trick to minimize a > similar expression w.r.t. matrix B with constraints? > > Thanks very much in advance. If possible send an e-mail to [EMAIL PROTECTED] > > Take care.
Chapter 6 of Graham's "Kronecker products and matrix calculus with applications", Ellis Horwood, Chichester, 1981, covers that topic (derivative of matrix wrt a matrix) at a fairly elementary level. Ordinary matrix products are not sufficient: the Kronecker product, introduced there in Chapter 2, is necessary. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
