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