How to calculate the derivative of matrix w.r.t another matrix?

*To*: mathgroup at smc.vnet.net*Subject*: [mg46704] How to calculate the derivative of matrix w.r.t another matrix?*From*: "Fred" <f0z6305 at labs.tamu.edu>*Date*: Tue, 2 Mar 2004 00:14:30 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Dear All I have a problem of calculating the derivative of dxm matrix A with respect to another dxm matrix B, where A= [a1 a2 ... am] and B =[b1 b2 ... bm] with ai and bj are vectors. Actually the matrix A itself is the first order derivative of a scalar J with respect to B, i.e., A = dJ/dB, where a1 = dJ/db1, a2 = dJ/db1, and so on. Now dA/dB is the second order derivative dA/dB = dJ^2/(dBdB') = [dJ/db1 dJ/db1 ... dJ/dbm]/d[b1 b2 ... bm]. So anybody have some idea on how to derive the formulation of dA/dB? Thanks for your point on this problem. Fred