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problem in minimization of a matrix

  • To: mathgroup at smc.vnet.net
  • Subject: [mg122866] problem in minimization of a matrix
  • From: Herman16 <btta2010 at gmail.com>
  • Date: Sun, 13 Nov 2011 04:43:24 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

\[Sigma]M[\[Rho]_, \[Phi]_] := 
 ArrayFlatten[
  Cosh[2 \[Rho]]/
   2 ({{1 + 
       Tanh[2 \[Rho]] Cos[\[Phi]], -Tanh [
         2 \[Rho]] Sin[\[Phi]] }, {-Tanh [2 \[Rho]] Sin[\[Phi]], 
      1 - Tanh[2 \[Rho]] Cos[\[Phi]]}})]

NMinimize[{\[Sigma]M[\[Rho], \[Phi]], \[Rho] >= 0, 
  0 <= \[Phi] <= 2 \[Pi]}, {\[Rho], \[Phi]}]

\[Tau][\[Alpha]_, \[Beta]_, \[Omega]0_, \[Lambda]_, t_, 
  r_, \[Rho]_, \[Phi]_] := 
 Det[At[\[Alpha], \[Beta], \[Omega]0, \[Lambda], t, r] - 
   Ct[\[Alpha], \[Beta], \[Omega]0, \[Lambda], t, r] 
    Inverse[(At[\[Alpha], \[Beta], \[Omega]0, \[Lambda], t, 
        r] + \[Sigma]M[\[Rho], \[Phi]])] 
    Ct[\[Alpha], \[Beta], \[Omega]0, \[Lambda], t, r]\[Transpose]]

But the matrix  At & Ct are depend on numbers, the minimization is on \
the matrix \[Sigma]M[\[Rho]_, \[Phi]_]



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