- #1
brushman
- 113
- 1
Homework Statement
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?
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 BThanks.