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. So I would appreciate pointers on how to go about this in a principled way, what to read, and an existing package to model mine after. Thanks!