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### Is there any theorem which guarantees the existence of an eigenvalue for a non-normal matrix in the vicinity of its perturbed matrix? [closed]

Let $A=(a_{ij})$ be a non-normal square matrix of order $n$ such that $a_{ji}=1/a_{ij}$ if
$a_{ij}\neq 0$ and $0$ otherwise. If $B$ is the perturbed matrix obtained from $A$ such that $B$ also ...