Given four complex matrices A, B, C and D where A ∈ Cn×n and D ∈ Cm×m and given two distinct arbitrary complex numbers λ1 and λ2, so that they are not eigenvalues of the matrix A, we find a nearest matrix from the set of matrices X ∈ Cm×m to matrix D (with respect to spectral norm) such that the matrix A B C X ! has two prescribed eigenvalues λ1 and λ2. 1. Introduction
