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Re: trouble with obtaining eigenvalue of parametric matrix

• To: mathgroup at smc.vnet.net
• Subject: [mg128394] [mg128394] Re: trouble with obtaining eigenvalue of parametric matrix
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Fri, 12 Oct 2012 00:01:27 -0400 (EDT)
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• References: <20121011060747.B7BE868A6@smc.vnet.net>

As the error message indicated, your list doesn't represent a matrix. A matrix is represented by a list consisting of lists, representing its rows, that all have the same length. Look at your list:

  mat = {{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}};

  Dimensions/@ mat
{{14}, {13}, {13}, {13}, {13}, {13}, {13}, {13}, {15}, {13}, {13}, \
{13}, {13}}

You can see the same thing is you inspect the output of:

  mat // MatrixForm

On Oct 11, 2012, at 2:07 AM, Mehrzad Sasanpoor <mz_spoor 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

---
Murray Eisenberg                                     
murray at math.umass.edu
Mathematics & Statistics Dept.      
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                  413 545-2859 (W)
710 North Pleasant Street                      fax   413 545-1801
Amherst, MA 01003-9305

• References:
  • trouble with obtaining eigenvalue of parametric matrix
    • From: Mehrzad Sasanpoor <mz_spoor@yahoo.com>