The Extremum of the Frobenius Norm of Matrix

For two given matrices A and B, the extremum of the Frobenius norm of matrix B-XA is established when X is running all over the unitary matrices. By using the technique of singular value decomposition, the extremum of the Frobenius norm matrix is studied. The result shows that the matrix B-XA has extremum when X is running all over the unitary matrices and in this paper, the bounded of maximum and the minimum of the Frobenius norm is obtained.