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?
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 a–xI is given by $\displaystyle |A-xI| = \begin{vmatrix}B-xI&C\\0&D-xI\end{vmatrix} = |B-xI||D-xI|$. This is zero if and only if x is an eigenvalue of either B or D.