# Eigenvalue of anti triangular block matrix (skew matrix?)

I have an real anti-triangular matrix

$M=\left[ \begin{array}{cc} A & B \\ I & 0 \\ \end{array} \right]$ where I is an identity matrix. $A$, $B$, $I$, $0$ are all square real matrix with the same dimention $n\times n$.

Qestions is, do eigenvalues of $M$ have specific relationships with submatrix $A$, $B$?

Any theroy or discussions would be helpful.

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Nope as your matrix doesn't need to have a single eigenvalue in general, look at the trivial case where $n=1$ and your blockmatrix is $\begin{pmatrix}0 & -1 \\ 1 & 0 \\ \end{pmatrix}$ As the characteristic polynomial is $x^2+1$ it doesn't have any eigenvalues over $\mathbb{R}$ while $A$ hast the eigenvalue $0$ and $B$ has the eigenavlue $-1$.