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Re: trouble with obtaining eigenvalue of parametric matrix

• To: mathgroup at smc.vnet.net
• Subject: [mg128395] [mg128395] Re: trouble with obtaining eigenvalue of parametric matrix
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Fri, 12 Oct 2012 00:01:47 -0400 (EDT)
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• References: <20121011060747.B7BE868A6@smc.vnet.net>

Length /@ {{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}}

{14, 13, 13, 13, 13, 13, 13, 13, 15, 13, 13, 13, 13}

Your first row has an extra comma causing a Null as a 14th element and
the ninth row has two extra entries (presumably extra zeros). Hence
the error message saying that your matrix is not square.


Bob Hanlon


On Thu, 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
>

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