How to solve for Gradient and Hessian of matrix expressions
- To: mathgroup at smc.vnet.net
- Subject: [mg8056] How to solve for Gradient and Hessian of matrix expressions
- From: Tinglun Song <song at wombat.eng.fsu.edu>
- Date: Mon, 4 Aug 1997 01:47:39 -0400
- Organization: Florida State University
- Sender: owner-wri-mathgroup at wolfram.com
Hi
I need to solve for the gradients and Hessian of a complex matrix
expressions with respect to certain matrix variables SYMBOLICALLY. For
example,
Given matrices A,B,C,Y (the only things I know are the dimensions of each
matrices involved and [A+B*Y*A] is invertible), I want to solve for the
gradient and Hessian of the following expressions with respect to Y
[A^T+B*C+A*Y]^{T} * [A+B*Y*A]^{-1} * [A^{T}+B*C+A*Y]
where ^{T} and ^{-1} denote the transpose and inverse of the matrices
concerned.
THANKS