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Re: problem in minimization of a matrix

• To: mathgroup at smc.vnet.net
• Subject: [mg123330] Re: problem in minimization of a matrix
• From: Herman <btta2010 at gmail.com>
• Date: Thu, 1 Dec 2011 08:03:58 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hi Peter,

My problem is that i want to minimize the determinant of the matrix \Tau over all values of the matrix \Sigma but couldn't understand

\[Sigma]M[\[Rho]_, \[Phi]_] = 
  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]]}});
I want to minimize this matrix \[Tau][\[Alpha]_, \[Omega]0_, t_, r_, \[Rho]_, \[Phi]_] = 
 FindMinimum[{Det[
    At[\[Alpha], \[Omega]0, t, 
      r] - (Ct[\[Alpha], \[Omega]0, t, r] 
       Inverse[(At[\[Alpha], \[Omega]0, t, 
           r] + \[Sigma]M[\[Rho], \[CurlyPhi]])] 
       Ct[\[Alpha], \[Omega]0, t, r]\[Transpose])], \[Rho] >= 0, 
   0 <= \[Phi] <= 2 \[Pi]}, {\[Rho], \[Phi]}] 

The matrx At & Ct are real numbers which depend on my choice of the parameters \alpha, \omega, t & r.  please write  if any things is unclear

Many thanks for any comment.

• Follow-Ups:
  • Re: problem in minimization of a matrix
    • From: DrMajorBob <btreat1@austin.rr.com>