Block diagonalization of a Square matrix by Orthogonal transformation?

Questions
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1

Hi all,

Is it possible to block diagonalize a square matrix using orthogonal transformation such that eigenvalues of the system matrix remain same. I have three matrices W, G and V where G is the system matrix. Now, matrix multiplication WGV is to be diagonalized by orthogonal transformation to get W_1G_1V_1 such that the the eigenvalues of G and G_1 remain same.

2

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