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Re: Numerical Determinants

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  • Subject: [mg13001] Re: Numerical Determinants
  • From: hello at (Rod Pinna)
  • Date: Tue, 30 Jun 1998 00:26:01 -0400
  • Organization: UWA
  • References: <6n4o6m$>
  • Sender: owner-wri-mathgroup at

Thanks for the reply. I eventually realised that I should be  using the
eigenvalue function, however, it turns out that for the  matricies I'm
examining, B is non-invertible. To get around this,  I've been using
the following:


This seems to be giving me the expected answers for A.x=p B.x, However,
I'm not convinced by the mathematics of it...

Thanks again though.

In article <6n4o6m$nin at>, Hugh Walker  <hwalker at>

>Yes, I have a suggestion.  Consider the eigen-problem -a.x = p b.x.
>Non-trivial eigenvectors exit provided Det[a + b p] = 0, which is your
>situation.  Assuming Inverse[b] exists, the eigen values of m.x = p x
>where m = -Inverse[b].a
>will coincide with your p's.
>I tested cases in which a and b are each random 10x10 matrices. The
>results were the same, and timings for the two approaches were
>Det = 9.0 sec
>eigen = 0.0 sec
>I hope this helps.
>Hugh Walker
>Professsor Emeritus
>University of Houston
>Gnarly Oaks

Rod Pinna
(rpinnaX at  Remove the X for email)

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