Let $B$ be a $2 \times 2$ matrix. Suppose we have a $4 \times 4$ real symmetric matrix of the following form
$$A = \begin{bmatrix} O_2 & B \\ B^T & O_2\\ \end{bmatrix}$$
What can we say about the eigenvalues of $A$?
Can we condition $B$ in a way such that the spectral radius of $A$ is less than $1$?
2026-03-25 14:27:01.1774448821
Spectral radius of a hollow symmetric block matrix
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