Re: Eigenvalue Problem
- To: mathgroup at smc.vnet.net
- Subject: [mg16897] Re: Eigenvalue Problem
- From: bruck at pacificnet.net (Ronald Bruck)
- Date: Tue, 6 Apr 1999 01:27:29 -0400
- Organization: University of Southern California
- References: <7e9odu$3km@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <7e9odu$3km at smc.vnet.net>, Peter Huesser <phuesser at bluewin.ch> wrote:
> Hello everybody
>
> I am trying to solve the eigenvalue problem for the following matrix:
>
> m = {{10 A, 0, B, 0, 0, 0},
> {0, -2 A, 0, C, 0, 0},
> {B, 0, -8 A, 0, C, 0},
> {0, C, 0, -8 A, 0, B},
> {0, 0, C, 0, -2 A, 0},
> {0, 0, 0, B, 0, 10 A}}
>
> which is symmetric. Now mathematica returns some complex eigenvalues
> which is not
> possible for a real, symmetric matrix. Can anybody help me ? Maybe the
> error occurs because
> mathematica means that the coefficients are complex but how can I make
> them real ?
>
> Thank's in advance for any help.
>
>
> Peter Huesser
The problem is that det (xI - m) is the square of a cubic polynomial.
Mathematica is using Cardano's formula, which often leads to complex
numbers--which cancel out, leaving only real numbers. This behavior CAN'T
be overcome, restricting yourself to algebraic functions. It is possible
to do it using trig functions, and I think that's documented somewhere.
It's appeared in this newsgroup before, certainly.
Try a web search on "cubic equation".
--Ron Bruck