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looking for a symbolic matrix calculus package


I'm looking for a Mathematica package to do symbolic matrix calculus, e.g.,
where one could declare vectors (x, y, ...) as having shape
n x 1, matrices (A, B, ...) as shape n x n, and get things like

Derivative[ a . x, x] ==> a
Derivative[ x . x, x] ==> 2 x
Derivative[ Transpose(x) . A . x, x] ==> 2 A . x

etc.
I have seen some packages for tensors and tensor calculus, but they
are way to complex for my needs.

A direct reply email would be appreciated. 

thanks,

--
Michael Friendly     Email: friendly at yorku.ca (NeXTmail OK)
Psychology Dept
York University      Voice: 416 736-5115 x66249 Fax: 416 736-5814
4700 Keele Street    http://www.math.yorku.ca/SCS/friendly.html
Toronto, ONT  M3J 1P3 CANADA


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