matrix identity pointers

• To: mathgroup at smc.vnet.net
• Subject: [mg77490] matrix identity pointers
• From: grenander at gmail.com
• Date: Sun, 10 Jun 2007 07:21:42 -0400 (EDT)

I would like to do symbolic matrix manipulations in Mathematica where
identities  like \partial{det(X)} = det(X) Tr(X^-1 \partial{X}), where
X is a matrix, would be known to Mathematica and used in things like
Simplify[]. There are many such useful identities. There is a nice
list in:

http://matrixcookbook.com/

I am a novice and I am guessing something like this has not been
implemented in Mathematica. There are lots of posts on related topics in this
group including how to define your own non-commutative algebras and
implementing replacement rules. There is a math source package on
exterior calculus and a draft book written with mathematica on
grassmanian algebras. There's an exercise in Michael Trott's book on
how to prove det(e^A)=e^tr(A) for 3x3 matrices. But I'm still not sure
how to start even though people have solved more difficult related
problems.