# Eigenvalues of triangular block matrix

I need to find an expression for determining the eigenvalues of this matrix block $$Acc=\begin{bmatrix} A & I \\ L & 0 \\ \end{bmatrix}$$ where

• $A$ is a matrix of size $n \times n$
• $L$ is a symmetric matrix of size $n \times n$
• $0$ is the null matrix of size $n \times n$
• $I$ is the identity matrix of size $n \times n$

Because the size of these matrices is very large and I have to carry out a program for calculating these eigenvalues I wish I could find a relationship relating the eigenvalues of $Acc$ and the eigenvalues of $A$ and $L$.

• There is some material here about Determinants of Block Matrices, and after reading it would seem to me that knowing the invertibility of $A$ is helpful..., though I'm not sure. – Eleven-Eleven Dec 8 '15 at 18:31
• Thanks, I had noticed that the question was not clear and I have update it for more details: – Luca Angelino Dec 8 '15 at 21:29
• Because the size of this matrix are very large and have to carry out a program for calculating these eigenvalues I wish I could find a relationship Brother eigenvalues of Acc and the eigenvalues of A and L – Luca Angelino Dec 8 '15 at 21:30
• with the properties of the determinants of wikipedia I have not been able to get useful results – Luca Angelino Dec 8 '15 at 21:31