论文标题
双$ r $ rank分解及其应用
Dual $r$-Rank Decomposition and Its Applications
论文作者
论文摘要
在本文中，我们介绍了双矩阵的双$ r $ rank分解，获得其存在状态和分解的等效形式，并得出了对双摩尔 - 螺旋属性逆（DMPGI）的一些特征。基于DMPGI，我们引入了一个特殊的双矩阵（双EP矩阵）。通过应用双$ r $ rank分解，我们得出了对双EP矩阵，双重掌握矩阵，双重概括性倒置以及双penrose方程之间的关系的几种特征。
In this paper, we introduce the dual $r$-rank decomposition of dual matrix, get its existence condition and equivalent form of the decomposition, as well as derive some characterizations of dual Moore-Penrose generalized inverse(DMPGI). Based on DMPGI, we introduce one special dual matrix(dual EP matrix). By applying the dual $r$-rank decomposition we derive several characterizations of dual EP matrix, dual idempotent matrix, dual generalized inverses, and the relationships among dual Penrose equations.
