$A$ is square symmetric matrix as:
$A=\begin{pmatrix} A_1&A_2 \\ A_3 & A_4 \end{pmatrix}$ I have two points which need help to understand clearly:
All blocks $A_1$, $A_2$, $A_3$, $A_4$ of symmetric $A$ are symmetric too. Is it right?
Is any relation between eigenvectors/eigenvalues of matrix $A$ and its blocks?
Thank you for your help.