Eigen value and eigen vector of a 2*2 block matrix
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syms a51 a53 a54 a56 a62 a65 a67 a68 a71 a73 a74 a76 a81 a83 a84 a86
C=[a51 0 a53 a54; 0 a62 0 0;a71 0 a73 a74;a81 0 a83 a84];
D=[ 0 a56 0 0;a65 0 a67 a68;0 a76 0 0;0 a86 0 0];
G=[A B;C D]
I want to find eigen value and eigen vector of Matrix G. I tried the code eig (G), but it not works.
For this matrix G, the characteristic polynomial can be reduced to a fourth order equation with the eigenvalues being the positive and negative square roots of the roots of that equation, But how this result help to find expresion for eigen value of G and also eigen vector (in terms of general eigen value e)?