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Re: trouble with obtaining eigenvalue of parametric matrix

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  • Subject: [mg128401] Re: trouble with obtaining eigenvalue of parametric matrix
  • From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
  • Date: Sat, 13 Oct 2012 01:03:19 -0400 (EDT)
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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

Hi, your matrix has different length of lines, and it is not equal to the length of the column.

Let us look. This is your matrix, as I copied it from your post:

m = {{ec, tc, tc, 0 , 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}};

This is the number of its sublists:

Length[m]

13

And this are the lengths of the sublists:

Map[Length, m]


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

As you see, the length of the first sublist is 14, that of the 9th is 15, while all the rest have 13 elements.
Therefore, your list does not represent a square matrix.

Have fun, Alexei

Alexei BOULBITCH, Dr., habil.
IEE S.A.
ZAE Weiergewan,
11, rue Edmond Reuter,
L-5326 Contern, LUXEMBOURG

Office phone :  +352-2454-2566
Office fax:       +352-2454-3566
mobile phone:  +49 151 52 40 66 44

e-mail: alexei.boulbitch at iee.lu






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