       Re: Numerical Determinants

• To: mathgroup at smc.vnet.net
• Subject: [mg13001] Re: Numerical Determinants
• From: hello at there.com (Rod Pinna)
• Date: Tue, 30 Jun 1998 00:26:01 -0400
• Organization: UWA
• References: <6n4o6m\$nin@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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:

1
--------------------------
Eigenvalues[Inverse[A]].B]

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 smc.vnet.net>, Hugh Walker  <hwalker at gvtc.com>
wrote:

>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
>
>Eigenvalues[-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 XcivilX.uwa.edu.au  Remove the X for email)

```

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