Given four complex matrices A, B, C and D where A ∈ C n×n and D ∈ C m×m and given two distinct arbitrary complex numbers λ 1 and λ 2 , so that they are not eigenvalues of the matrix A, we find a nearest matrix from the set of matrices X ∈ C m×m to matrix D (with respect to spectral norm) such that the matrix A B C X has two prescribed eigenvalues λ 1 and λ 2.