core-EP矩阵的性质与二元关系
Properties of core-EP matrices and binary relationships
AI总结：
本文通过引入与$A$相关的MPDMP矩阵刻画core-EP矩阵，研究MPD、DMP、CMP逆及相关二元关系序，并证明core-EP矩阵类中DMP、MPD与Drazin逆相等。
摘要：
本文研究了core-EP矩阵的各种性质。我们引入了与$A$相关的MPDMP矩阵，并借助它得到core-EP矩阵的一些性质和等价条件。此外，还研究了MPD逆、DMP逆和CMP逆的性质，并证明在core-EP矩阵类中，DMP逆、MPD逆和Drazin逆是相同的。另外，引入了DMP和MPD二元关系序，并考察了这些序与其他二元关系序之间的关系。
英文摘要：
In this paper, various properties of core-EP matrices are investigated. We introduce the MPDMP matrix associated with $A$ and by means of it, some properties and equivalent conditions of core-EP matrices can be obtained. Also, properties of MPD, DMP, and CMP inverses are studied and we prove that in the class of core-EP matrices, DMP, MPD, and Drazin inverses are the same. Moreover, DMP and MPD binary relation orders are introduced and the relationship between these orders and other binary relation orders are considered.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
