Thread: 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?

Originally Posted by Susaluda

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 . This is zero if and only if x is an eigenvalue of either B or D.