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Help with minimization of Eigenvalues

  • To: mathgroup at smc.vnet.net
  • Subject: [mg87747] Help with minimization of Eigenvalues
  • From: Chimico <Dario.Bressanini at gmail.com>
  • Date: Wed, 16 Apr 2008 06:50:22 -0400 (EDT)

Hi,

I am trying to minimize a particular eigenvalue of a generalized
eigenvalue problem that depends on a few parameters. I have the
following problem:

Suppose we have two matrices s and m like these (the real matrices are
much more complicated)

m = {{a, b}, {b, -a + 1}}

s = {{1, 0}, {0, 3a}}

If I define the function Eig

Eig[a_, b_] := Eigenvalues[{m, s}]//First

And use it with the FindMinimum function it does not work.
Infact just calling

Eig[1,2] gives the error

Eigenvalues::gfargs:
   Generalized Eigenvalues
     arguments accept only matrices with machine real
      and complex elements. More...

Even inserting Evaluate[] into the Eigenvalues function does not work.
What am I doing wrong?
Any help would be appreciated :-)
thanks  Dario



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