Inverse eigenproblem for centrosymmetric and centroskew matrices and their approximation (Q598203)

The authors examine the inverse eigenvalue problem of recovering a centrosymmetric or centroskew symmetric \(n\times n\) matrix from a given set of \(m\) eigenvalues \(\left\{ \lambda _{i}\right\} _{i=1}^{m}\) and their \(m\) corresponding eigenvectors \(\left\{ X_{j}\right\} _{j=1}^{m}\) in \(C^n\). Recall that \(A\) is a centrosymmetric matrix if it satisfies \(A=J_{n}AJ_{n}\;\) where \(J_{n}\) is an anti-identity. The problem of finding the best approximation is also considered.