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I need to find the λ and the ai that solves the Generalized eigenvalue problem

[A]{a}=-λ^{2}{a}

with

[A]=

andCode (Text):

-1289.57,1204.12,92.5424,-7.09489,-25037.4,32022.5,-10004.3,3019.17

1157.46,-1077.94,-0.580522,-78.9482,32022.5,-57353.5,36280.6,-10949.6

166.577,-103.776,1494.41,-1557.21,-10004.3,36280.6,-63053.2,36776.9

-34.4753,-22.407,-1586.37,1643.25,3019.17,-10949.6,36776.9,-28846.5

-22840.1,29254.3,-9328.5,2914.31,-1289.57,1157.46,166.577,-34.4753

29254.3,-51067,31724.8,-9912.15,1204.12,-1077.94,-103.776,-22.407

-9328.5,31724.8,-54591.9,32195.6,92.5424,-0.580522,1494.41,-1586.37

2914.31,-9912.15,32195.6,-25197.7,-7.09489,-78.9482,-1557.21,1643.25

=

Using mathematica I get for lambdas {75.1098, 35.2687, 34.3082, 15.2013, 4.3281, 1.35478,Code (Text):

0,0,0,0,1875.81,0,0,0

0,5019.07,0,0,0,22535.3,0,0

0,0,-5019.07,0,0,0,22535.3,0

0,0,0,0,0,0,0,937.905

835.2,0,0,0,0,0,0,0

0,5003.02,0,0,0,5019.07,0,0

0,0,5003.02,0,0,0,-5019.07,0

0,0,0,417.6,0,0,0,0

5.38827*10^-154, -2.06904*10^-154}

The last two eigenvalues are zero. That made me think that two equations are redundant. I confirmed that with mathematica. Rank of A is 6.

How can I reduce the system? I tried deleting two rows and columns, but for all the combinations the matrix B is singular.

Notice that the first and last column/row of the matrix B have only one value different from zero. Is anything I can do to exploit that?

Best

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# Generalized Eigenvalue problem

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