MathGroup Archive 1997

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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



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