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MathGroup Archive 2004

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Re: Symbolic matrix algebra

  • To: mathgroup at
  • Subject: [mg45479] Re: Symbolic matrix algebra
  • From: Sotirios Bonanos <sbonano at>
  • Date: Fri, 9 Jan 2004 05:20:50 -0500 (EST)
  • Organization: National Technical University of Athens, Greece
  • References: <bti1i1$a6p$>
  • Reply-to: sbonano at
  • Sender: owner-wri-mathgroup at

"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
(, 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

Good luck!
S. Bonanos

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