Re: Eigenvalue Problem

• To: mathgroup at smc.vnet.net
• Subject: [mg16952] Re: Eigenvalue Problem
• From: Pierre infelta <pierre.infelta at epfl.ch>
• Date: Thu, 8 Apr 1999 02:32:47 -0400
• Organization: EPFL
• References: <7e9odu\$3km@smc.vnet.net> <7ef0d5\$c4f\$4@dragonfly.wolfram.com>
• Sender: owner-wri-mathgroup at wolfram.com

```try
Needs["Miscellaneous`RealOnly`"]

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}}
The answer replaces the nonreal roots by nonreal.

Ed McBride 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 ?
>
> I get the same phenomenon.  And I also got it with a 3 x 3 I made up.  I
> presume the results turn out to be real if a,b,c are real, but they are
> too complicated to prove this without a bunch of work.  Sorry, Ed
> McBride

```

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