Re: Eigenvalues
- To: mathgroup@smc.vnet.net
- Subject: [mg11522] Re: Eigenvalues
- From: Paul Abbott <paul@physics.uwa.edu.au>
- Date: Fri, 13 Mar 1998 12:22:11 -0500
- Organization: University of Western Australia
- References: <6e88nh$nok@smc.vnet.net>
Raya Khanin wrote:
> I have a problem of calculating eigenvalues for a simple 4X4 matrix. I
> am working on Sun workstation, and it takes minutes and minutes for
> Mathematica to perform Eigenvalues[] operation for a matrix like this
>
> Clear[a, b, c, d, e, d, f, g];
> testmatrix = {{a, b, c, d}, {b, c, d, e}, {c, d, e, f}, {d, e, f, g}};
> Eigenvalues[testmatrix];
>
> I will need to work with much larger (symbolic) matrices with not that
> simple entries. Has anyone had an experience of working with symbolic
> matrices?
If you do the following,
In[1]:= SetOptions[Roots, Cubics->False, Quartics->False];
you will find that Eigenvalues[testmatrix] is significantly faster.
However, what possible use can you have for the symbolic eigenvalues for
arbitrarily large symbolic matrices? (I am aware of no simplifying
identites for nxn Toeplitz matrices)
>Would it be better doing this in MatLab?
In general, for an arbitrary symbolic matrix, the best result you can
hope for is an expression for the eigenvalues in terms of the roots of
the characteristic polynomial.
I'd be most interested to hear how MatLab fares with this problem ...
Cheers,
Paul
____________________________________________________________________
Paul Abbott Phone: +61-8-9380-2734
Department of Physics Fax: +61-8-9380-1014
The University of Western Australia Nedlands WA 6907
mailto:paul@physics.uwa.edu.au AUSTRALIA
http://www.pd.uwa.edu.au/~paul
God IS a weakly left-handed dice player
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