Re: symbolic matrix inverse
- To: mathgroup at smc.vnet.net
- Subject: [mg94227] Re: symbolic matrix inverse
- From: magma <maderri2 at gmail.com>
- Date: Mon, 8 Dec 2008 06:23:36 -0500 (EST)
- References: <ghb014$ogk$1@smc.vnet.net>
On Dec 5, 11:33 am, Steven Allmaras <steven.r.allma... at boeing.com>
wrote:
> I have a symbolic matrix {{a,b},{c,d}} whose elements are themselves matr=
ices. The elements are noncommutative (e.g., a.b != b.a), and just for=
simplicity assume each element is a n-by-n square matrix of reals. How =
do I get Mathematica to evaluate Inverse[{{a,b},{c,d}}] in terms of Dot and=
Inverse, rather than Times and Divide? I'm hoping to get something that=
looks like,
>
> [[1,1]] = Inverse[a] + Inverse[a].b.Inverse[d - c.Inverse[a].b].c.Inver=
se[a]
>
> Thanks,
> Steve
I do not think you can overload the existing Inverse function so that
it works with Dot or Composition or that in general that it works with
matrices in a non-commutative ring.
I believe the only solution is to define your own Inverse function
(better perhaps call it something else) along the outline that you
posted.
I suggest that you consider looking at Composition , InverseFunction
and Working with Operators sections in the documentation.
hth