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Re: trouble with obtaining eigenvalue of parametric matrix

  • To: mathgroup at smc.vnet.net
  • Subject: [mg128385] [mg128385] Re: trouble with obtaining eigenvalue of parametric matrix
  • From: "Dr. Wolfgang Hintze" <weh at snafu.de>
  • Date: Thu, 11 Oct 2012 23:58:26 -0400 (EDT)
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On 11 Okt., 08:15, Mehrzad Sasanpoor <mz_sp... at yahoo.com> wrote:
> I have a parametric 13*13 matrix as following and I want to find their eigenvalues in term of these parameters.
>
> Eigenvalues[{{ec,
> tc, tc, ,0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {tc, ec, 0, tc, 0, 0, 0, 0, 0, 0, 0, 0,
> 0}, {tc, 0, ec, 0, tc, 0, 0, 0, 0, 0, 0, 0, 0}, {0, tc, 0, ec, 0, tc, zc, xc, 0,
> 0, 0, 0, 0}, {0, 0, tc, 0, ec, tc, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, tc, tc, ec, 0,
> 0, 0, 0, 0, 0, 0} ,{0, 0, 0, zc, 0, 0, ez, 0, 0, 0, 0, 0, 0}, {0, 0, 0, xc, 0, 0,
> 0, ex, 0, xo, xy, xo, xy}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ey, nyx, yy, yx, yy},
> {0, 0, 0, 0, 0, 0, 0, xo, nyx, ex, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, xy, yy, 0, ey,
> 0, 0}, {0, 0, 0, 0, 0, 0, 0, xo, nyx, 0, 0, ex, 0}, {0, 0, 0, 0, 0, 0, 0, xy, yy,
> 0, 0, 0, ey}}]
>
> but I face with this error?
>
> Eigenvalues::matsq: Argument \
> {{ec,tc,tc,0,0,0,0,0,0,0,<<3>>},{tc,ec,0,tc,0,0,0,0,0,0,<<3>>},{tc,0,\
> ec,0,tc,0,0,0,0,0,<<3>>},<<5>>,{0,0,0,0,0,0,0,0,0,0,<<5>>},{0,0,0,0,0,\
> 0,0,xo,nyx,ex,<<3>>},<<3>>} at position 1 is not a nonempty square \
> matrix. >>
>
> what should I do?
>
> thanks a lot for your attention

There were simply some typos in your matrix.

I corrected (by brute force) the lines with a length different from 13
with the result:

In[73]:= m = {{ec, tc, tc, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {tc, ec, 0,
    tc, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {tc, 0, ec, 0, tc, 0, 0, 0, 0, 0,
    0, 0, 0},
       {0, tc, 0, 0, ec, tc, zc, xc, 0, 0, 0, 0, 0}, {0, 0, tc, 0,
    ec, tc, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, tc, tc, ec, 0, 0, 0, 0,
    0, 0, 0},
       {0, 0, 0, zc, 0, 0, ez, 0, 0, 0, 0, 0, 0}, {0, 0, 0, xc, 0, 0,
    0, ex, 0, xo, xy, xo, xy}, {0, 0, 0, 0, 0, 0, 0, 0, ey, nyx, yy,
    yx, yy},
       {0, 0, 0, 0, 0, 0, 0, xo, nyx, ex, 0, 0, 0}, {0, 0, 0, 0, 0,
    0, 0, xy, yy, 0, ey, 0, 0}, {0, 0, 0, 0, 0, 0, 0, xo, nyx, 0, 0,
    ex, 0},
       {0, 0, 0, 0, 0, 0, 0, xy, yy, 0, 0, 0, ey}};

Checkin the lengths using:
In[74]:= (Length[m[[#1]]] & ) /@ Range[13]
Out[74]= {13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13}

Looking at the appearance of the matrix using
In[75]:= MatrixForm[m]

An finally determining the Eigenvalues (I have supressed the very long
output)
In[76]:= Eigenvalues[m]

Hope this helps.

Regards,
Wolfgang



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