Re: Symbolic matrix algebra

• To: mathgroup at smc.vnet.net
• Subject: [mg45479] Re: Symbolic matrix algebra
• From: Sotirios Bonanos <sbonano at inp.demokritos.gr>
• Date: Fri, 9 Jan 2004 05:20:50 -0500 (EST)
• Organization: National Technical University of Athens, Greece
• References: <bti1i1\$a6p\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```"mike.james" wrote:

> This is a very silly question and I have checked the archives for anything
> relevant - I must just be searching on the wrong keywords.
>
> All I want to do is some simple matrix algebra.
> I want to type in  (A+B)^2 and have it expanded taking account of the fact
> that A and B are matrices.
> I want to use transpose, inverse and apply conditions such as the matrix is
> symmetric etc?
> I've tried non-commutive multiply and a few other tricks.
> I can see that I could write a package but surely there must be one or a
> built in solution I'm missing?
> mikej

You may want to try my "Exterior Differential Calculus" package
(http://www.inp.demokritos.gr/~sbonano/EDC/), which allows the user to define
arbitrary symbols (like A, B) that will be treated as matrices. The package
uses the symbol "[Wedge]" for matrix multiplication, and contains definitions
for symbolic application of trace rules and the Cayley-Hamilton theorem (see
examples in  EDC_Manual.nb and in  matrixEDCexamples.nb). For
suggestions as
to how to apply a symbolic inverse function see subsection "Introducing Custom
Notation" of the Manual.

The basic package is also available on MathSource
(http://library.wolfram.com/infocenter/MathSource/683).

Good luck!
S. Bonanos

```

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