關于矩陣廣義BottDuffin逆的逆序律

曹志強 杜乃林

摘 要： 研究了兩個Lp.s.d.矩陣廣義BottDuffin逆的逆序律問題，Lp.s.d.是半正定概念的一種推廣，正定或半正定矩陣恰是R np.s.d.矩陣.通過建立廣義BottDuffin逆與A（2）S，S⊥逆之間的關系，利用A（2）S，S⊥的性質，得到了廣義BottDuffin逆序律成立的充要條件，并通過兩個實例驗證了所得結果.

關鍵詞： 逆序律; Lp.s.d.矩陣; 廣義BottDuffin逆

中圖分類號： O 151.21? 文獻標志碼： A? 文章編號： 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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（責任編輯：馮珍珍）