D. E. Ferreyra, F. E. Levis, A. N. Priori, N. Thome
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引用次数: 0
Abstract
It is well known that a square complex matrix is called EP if it commutes with its Moore–Penrose inverse. In this paper, new classes of matrices which extend this concept are characterized. For that, we consider commutative equalities given by matrices of arbitrary index and generalized inverses recently investigated in the literature. More specifically, these classes are characterized by expressions of type \(A^mX=XA^m\), where X is an outer inverse of a given complex square matrix A and m is an arbitrary positive integer. The relationships between the different classes of matrices are also analyzed. Finally, a picture presents an overview of the overall studied classes.
众所周知，如果一个正方形复矩阵与它的摩尔-彭罗斯逆矩阵相乘，那么它就被称为 EP。本文阐述了扩展这一概念的新一类矩阵。为此，我们考虑了由任意指数矩阵和最近在文献中研究的广义逆矩阵给出的换元等式。更具体地说，这些类别的特征是 \(A^mX=XA^m/)类型的表达式，其中 X 是给定复方阵 A 的外逆，m 是任意正整数。此外，还分析了不同类别矩阵之间的关系。最后，一幅图片展示了所研究的所有类别的概况。
期刊介绍：
aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.
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