论文标题
双索引和双核概括逆
The Dual Index and Dual Core Generalized Inverse
论文作者
论文摘要
在本文中，我们介绍了双索引和双核概括逆（DCGI）。通过应用等级方程，广义逆和矩阵分解，当双重指数等于一个时，我们给出了几个表征。如果存在DCGI，我们会明白，它是唯一的。我们为DCGI提供了一个紧凑的公式，以及一系列逆存在的表征。 $ \ hat {m} $的双重索引等于一个且仅当其DCGI存在时，这是无值得的。当$ \ hat {m} $的双索引等于一个时，我们研究双Moore-Penrose概括性逆（DMPGI）和双组概括（DGGI），并考虑DCGI，DMPGI，DGGI，DGGI，MOORE-PENROSE DIM DIAL PERMATION（MOROER-PENE）之间的关系。此外，我们考虑对称双矩阵及其双重概括性对反面。最后，给出了两个示例，以说明DCGI在线性双方程中的应用。
In this paper, we introduce the dual index and dual core generalized inverse (DCGI). By applying rank equation, generalized inverse and matrix decomposition, we give several characterizations of the dual index when it is equal to one. And we get that if DCGI exists, then it is unique. We derive a compact formula for DCGI and a series of equivalent characterizations of the existence of the inverse. It is worth nothing that the dual index of $\hat{M}$ is equal to one if and only if its DCGI exists. When the dual index of $\hat{M}$ is equal to one, we study dual Moore-Penrose generalized inverse (DMPGI) and dual group generalized inverse (DGGI), and consider the relationships among DCGI, DMPGI, DGGI, Moore-Penrose dual generalized inverse (MPDGI) and other dual generalized inverses. In addition, we consider symmetric dual matrix and its dual generalized inverses. At last, two examples are given to illustrate the application of DCGI in linear dual equations.
