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Re: trouble with obtaining eigenvalue of parametric matrix

  • To: mathgroup at smc.vnet.net
  • Subject: [mg128388] [mg128388] Re: trouble with obtaining eigenvalue of parametric matrix
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Thu, 11 Oct 2012 23:59:27 -0400 (EDT)
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On 10/11/12 at 2:07 AM, mz_spoor at yahoo.com (Mehrzad Sasanpoor) 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. >>

Which is telling you you have *not* entered a 13 x 13 matrix.
Specifically, if I copy and paste your input and do:

In[1]:= x = {{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}};

In[2]:= Complement[Range[13], Pick[Range[13], Length /@ x, 13]]

Out[2]= {1,9}

Row 1 has an extra comma after the third element making this row
14 elements long. And row 9 is 15 elements long. Likely you've
entered extra leading zeros




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