Re: Matrix Inversion Method ?
- To: mathgroup at smc.vnet.net
- Subject: [mg9794] Re: Matrix Inversion Method ?
- From: Daniel Lichtblau <danl>
- Date: Fri, 28 Nov 1997 05:35:09 -0500
- Organization: Wolfram Research, Inc.
- Sender: owner-wri-mathgroup at wolfram.com
Norbert Scherm wrote:
>
> Hello,
>
> I would like to know which inversion method is applied by Mathematica
> when it computes the inverse of a symbolic matrix
>
> Mat={{a,b,c},{d,e,f},{g,h,i}}; .
>
> Taking a look at the result of Inverse[Mat]; may lead to the assumtion
> that something like
>
> adjugate[Mat]/Det[Mat]
>
> is used ???
>
> ('adjugate' (adjoint) stands for a matrix whose elements are signed
> cofactors or minor determinants)
>
> Thanks in advance,
>
> (Norbert) scherm at irt.uni-hannover.de
The default Metod->Automatic will indeed use CofactorExpansion as the
default method for Inverse. This is done up to some dimension (I think
11 x 11). Beyond this we row reduce to bring the dimension down, but it
is generally hopeless.
Depending on the structure of your symbolic matrix (sparsity, types of
entries, etc.) you might obtain reasonable results using the other
built-in methods OneStepRowReduction or DivisionFreeRowReduction.
Daniel Lichtblau
Wolfram Research