Abstract: In order to reduce the scale of the matrix and improve the computational efficiency of the large matrix, rank properties of Schur complement of the matrix under the addition and multiplication are analysed by using the theoretical knowledge of the matrix Schur complement and the rank inequality of matrix product. The inequality between the rank of Schur complement and the rank of the subgroup power, the inequality between the rank of the matrix power and the rank of Schur complement matrix, and rank inequality of the matrices sum under Schur complement are obtained.