一类特殊分块矩阵的Drazin逆
Drazin Inverses of a Special Class of Block Matrices
DOI: 10.12677/pm.2026.162032, PDF,    科研立项经费支持
作者: 盘子洋*, 秦莹莹#：五邑大学数学与计算科学学院，广东 江门
关键词: Drazin逆；群逆；正序律；分块矩阵；秩等式；Drazin Inverse； Group Inverse； Forward Order Law； Block Matrix； Rank Equality
摘要: Drazin逆是矩阵理论中不可或缺的一部分，在众多应用领域中具有重要的作用。本文通过应用两个矩阵乘积的Drazin逆的正序律，研究了秩可加性条件下一类2 × 2分块矩阵的Drazin逆，给出了其Drazin逆的若干新表达式。
Abstract: Drazin inverse is an indispensable part of matrix theory and plays an important role in many application fields. This article studies the Drazin inverse of a class 2 × 2 block matrix under rank additivity conditions, by applying the forward order law for Drazin inverse of the product of two matrices. In addition, we present some new representations of the Drazin inverse of these 2 × 2 block matrices with some rank additivity conditions.
文章引用：盘子洋, 秦莹莹. 一类特殊分块矩阵的Drazin逆[J]. 理论数学, 2026, 16(2): 32-38. https://doi.org/10.12677/pm.2026.162032

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