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