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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.

way, what to read, and an existing package to model mine after.

Thanks!



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