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 ____________________________________________________________________