Re: Eigenvalues
- To: mathgroup@smc.vnet.net
- Subject: [mg11550] Re: Eigenvalues
- From: "William F. Campbell" <valentin@wam.umd.edu>
- Date: Sat, 14 Mar 1998 13:56:04 -0500
- Organization: UMD Dept. of Meteorology
- References: <6e88nh$nok@smc.vnet.net>
Raya Khanin wrote:
> Hi,
>
> 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?
>
> Any suggestions will be appreciated!
>
> thanks a lot.
>
> Raya Khanin
The problem you have specified is quite difficult, and in fact,
if the matrix is 5x5 or larger, there
is no guarantee of a solution at all. Think about the characteristic
equation of the matrix you want to define. If it's a quintic or
higher, you're going to have problems solving it in closed form. If
your symbolic matrices are sparse, and/or have special symmetry
properties, you may be okay.
--
Bill Campbell Correlation is not cause.