# Computing Eigenvalues of a large matrix

Let's say a matrix M is composed of:

$$\begin{bmatrix} A & B \\ C & D \end{bmatrix}$$ where $$A \in \mathbb{R}^{n \times n}, B \in \mathbb{R}^{n \times m}, C \in \mathbb{R}^{m \times n},$$ and $$D \in \mathbb{R}^{m \times m}$$.

I would like to determine whether all eigenvalues in this matrix are positive (or there is an imaginary part).

I know that $$A$$ and $$D$$ are invertible. While I tried to make use of Schur complement, it requires $$B = C^T$$, which does not satisfy in my case. Do you have any recommendation on how to proceed from this step? Thank you very much!