Computational aspect to the nearest southeast submatrix that makes multiple a prescribed eigenvalue

Given four complex matrices A, B, C and D where A 2 Cnn and D 2 Cmm and let the matrix ( A B C D ) be a normal matrix and assume that is a given complex number that is not eigenvalue of matrix A. We present a method to calculate the distance norm (with respect to 2-norm) from D to the set of matrices X 2 Cmm such that, be a multiple eigenvalue of matrix (A BC X) . We also nd the nearest matrix X to the matrix D.