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MathGroup Archive 2004

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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



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