Re: Eigenvalue Problem
- To: mathgroup at smc.vnet.net
- Subject: [mg16991] Re: Eigenvalue Problem
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Sat, 10 Apr 1999 02:13:30 -0400
- Organization: University of Western Australia
- References: <7e9odu$3km@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Peter Huesser wrote:
> 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 ?
It can be shown that the (repeated) eigenvalues of this matrix can be
expressed in the explicitly real form,
2 2 2 1
(2 Sqrt[84 A + B + C ] Cos[- Pi (2 n - 1) +
3
2 2 2
1 3 Sqrt[3] A (80 A + B - 5 C )
- ArcCos[-(-------------------------------)]]) / Sqrt[3]
3 2 2 2 3/2
(84 A + B + C )
where n=1,2,3.
For a discussion of this problem, see
ftp://ftp.physics.uwa.edu.au/pub/Mathematica/MathGroup/RealRoots.nb
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 at physics.uwa.edu.au
AUSTRALIA http://www.physics.uwa.edu.au/~paul
God IS a weakly left-handed dice player
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