Wednesday, 11 December 2013

Eigenvalues of block diagonal matrix

I have a block-diagonal matrix of the form

$$
\begin{align*}
\bf{M} = \begin{bmatrix}
\bf{0} & \bf{I} \\
\bf{A} & \bf{B}
\end{bmatrix}
\end{align*}
$$

Can we say anything about the eigenvalues of $\bf{M}$ in terms the eigenvalues of the block matrices?




Here, $\bf{0}$ is a matrix of zeros and $\bf{I}$ is an identity matrix.



This is not in block upper/lower triangular form.

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