中文摘要：

广义逆理论是应用十分广泛的一个数学分支,它在线性代数、矩阵分析、矩阵理论、最优化和数理统计等研究领域有着极其重要的应用.本文利用广义Schur补的最大秩理论和一些经典的秩等式,研究了两个矩阵乘积的{1,3}逆的正序律,得出了正序律{1,3}A2 {1,3} ∈（AIA2）{1,3}成立的充要条件.

英文摘要：

The generalized inverse theory is a widely used branch of mathematics which has a wide range of applications in linear algebra, matrix analysis, matrix theory, optimization and mathematical statistics. In this paper, we study the forward order law for{1,3}-inverse of the product of two matrices by using the expressions for maximal ranks of the generalized Schur complement and some necessary and sufficient conditions for Aa {1,3}A2 {1,3} ∈（AIA2）{1,3} are obtained.