关于矩阵广义BottDuffin逆的逆序律

曹志强 杜乃林

摘 要： 研究了两个Lp.s.d.矩阵广义BottDuffin逆的逆序律问题，Lp.s.d.是半正定概念的一种推广，正定或半正定矩阵恰是R np.s.d.矩阵.通过建立广义BottDuffin逆与A（2）S，S⊥逆之间的关系，利用A（2）S，S⊥的性质，得到了广义BottDuffin逆序律成立的充要条件，并通过两个实例验证了所得结果.

关键词： 逆序律; Lp.s.d.矩阵; 广义BottDuffin逆

中图分类号： O 151.21  文献标志码： A  文章编号： 10005137（2019）04034709

Abstract： In this paper we investigate the reverse order law for the generalized BottDuffin inverses of two Lp.s.d.matrices.The concept of Lp.s.d.matrices is a generalization of semipositive definiteness，in the sense that Rnp.s.d.matrices are exactly semipositive definite matrices.We establish a relationship between generalized BottDuffin inverses and A（2）S，S⊥ inverses，and by using their properties，give necessary and sufficient conditions for the reverse order law of the generalized BottDuffin inverses.In the end we give two explicit examples to test our results.

Key words： reverse order law; Lp.s.d.matrix; generalized BottDuffin inverse

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