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