Nearest southeast submatrix that makes multiple an eigenvalue of the normal northwest submatrix (Q2885132)

Let \(A \in \mathbb{C}^{n\times n},~B \in \mathbb{C}^{n\times m},~C\in \mathbb{C}^{m\times n},~D\in \mathbb{C}^{m\times m}\), \(A\) be normal and \(z_0\) be a fixed eigenvalue of \(A\). Inspired by \textit{A. N. Malyshev} [Numer. Math. 83, No. 3, 443--454 (1999; Zbl 0972.15011)] and \textit{M. Wei} [Linear Algebra Appl. 280, No. 2-3, 267--287 (1998; Zbl 0936.65049)] regarding Wilkinson's problem, the authors find the distance (in the \(2\)-norm) from \(D\) to the set of \(m\times m\) matrices \(X\) such that \(z_0\) is a multiple eigenvalue of the matrix \(\left[\begin{matrix} A & C \\ B & X \end{matrix}\right]\).