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