The interior and closure of strongly stable matrices (Q1184472)

A real square matrix \(A\) is called strongly stable (resp. strongly semistable) if the eigenvalues of \(A+D\) have positive (resp. nonnegative) real parts for every nonnegative diagonal matrix \(D\). It is proved that the closure of the set of strongly stable matrices coincides with the set of strongly semistable matrices. Furthermore, the interior of the set of strongly stable matrices coincides with the set of matrices \(A\) having the property that all principal submatrices of \(A\) are strongly stable.