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Suppose $A$ is a random real-valued $n\times n$ matrix and we want to know the difficulty of solving $Ax=b$ when entries of $b$ are sampled IID from Normal$(0,1)$. Can we say anything about the ...

Let $H$ be an $n\times n$ Hermitian matrix and $A$ an $n\times n$ anti-Hermitian matrix, i.e. $H^\dagger = H$, $A^\dagger = -A$. Consider their sum $S= H+A$. Let $\{\sigma_i(S)\}_{i=1,\dots,r}$ denote ...