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MathGroup Archive 2004

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Symbolic matrix manipulation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46722] Symbolic matrix manipulation
  • From: junk4 at microserf.org.uk (C Rose)
  • Date: Tue, 2 Mar 2004 19:10:27 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi all

I wonder if anyone can help---I'm new to Mathematica.

I'd like to know how one can perform symbolic matrix-vector
manipulations in Mathematica, without having to specify the contents
of the matrices or vectors.

For example, imagine I have a vector-valued function

f(x) = x^T A

where A is a m x n matrix, x is an m-vector, and ^T indicates
transposition

How can I differentiate f(x)---or perform other symbolic operations
using matrices or vectors---such that I get the result in terms of A
and x (i.e. I don't want to have to specify that
A={{a11, a12, a13}, {a21, a22, a23}, {a31, a32, a33}} or whatever).

So, in the example above, I want Mathematica to tell me the answer is

d/dx (f) = A

I'd appreciate your advice on this matter.

Thanks, 

Chris


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