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Math Help - Eigenvalues of a block matrix?

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    Eigenvalues of a block matrix?

    Consider a 4x4 matrix A = [B C]
    ______________________[0 D],
    where B, C, D are 2x2 matrices. What is the relationship between eigenvalues of A, B, C, and D?
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    Quote Originally Posted by Susaluda View Post
    Consider a 4x4 matrix A = [B C]
    ______________________[0 D],
    where B, C, D are 2x2 matrices. What is the relationship between eigenvalues of A, B, C, and D?
    The determinant of axI is given by |A-xI| = \begin{vmatrix}B-xI&C\\0&D-xI\end{vmatrix} = |B-xI||D-xI|. This is zero if and only if x is an eigenvalue of either B or D.
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