QR decomposition and algorithm for unitary symmetric matrix

This paper discusses the quantitative correspondence of Q and R matrices of unitary symmetric matrices and its mother matrix. Based on definition of orthogonal counterbalance, authors definite the unitary counterbalance of matrix and prove the unitary counterbalance properties of unitary symmetric matrix and it's mother matrix, obtain some results as the Moore-Penrose inverses of unitary symmetric matrices are unitary counterbalance if unitary symmetric matrices are unitary counterbalance. At same time, authors give the algorithm of QR decomposition and Moore-Penrose inverses of unitary symmetric matrices.