1. The problem statement, all variables and given/known data Consider a 4 x 4 matrix A = B C 0 D where B, C, and D are 2 x 2 matrices. What is the relationship between the eigenvalues of A, B, C, and D? 3. The attempt at a solution I suppose you can write A as: b1 b2 c1 c2 b3 b4 c3 c4 0 0 d1 d2 0 0 d3 d4 and then find the eigenvalues of all of them in terms of those variables, but that seems like a lot of work that might not pay off. I know the characteristic equation for a 2x2 can be written (as follows) but I don't know what to do with it. λ^2 - trB λ + det B Thanks.