Eigenvalues of matrices with given block upper triangular part
Necessary and sufficient conditions are given for the existence of a matrix \(X\in \mathbb{C}^{m\times n}\) for which \(\lambda_1, \dots, \lambda_{n+m}\) are the eigenvalues of the \((n+m) \times (n+m)\) matrix \(M_X= M_X (A, B, C)\) defined by \[ M_X= {{A\;C} \brack {X\;B}}, \] where \(A\in \mathbb{C}^{n \times n}\), \(B\in \mathbb{C}^{m \times m}\) and \(C\in \mathbb{C}^{n \times m}\) are given complex matrices and \(\lambda_1, \dots, \lambda_{n+m}\) are given complex numbers.
matrices with given block upper triangular part
scientific article; zbMATH DE number 881694