ABSTRACT

The paper investigates the class of square matrices which have idempotent Moore–Penrose inverse. A number of original characteristics of the class are derived and new properties identified. Additionally, some isolated results scattered in the literature are recaptured and rederived in an extended or generalized form. The research was inspired by some matrix equations (occurring, e.g. in physics) which either directly involve matrices with an idempotent Moore–Penrose inverse or whose solvability under the assumption that the matrices involved have an idempotent Moore–Penrose inverse provides an emerging insight into the corresponding theory.

中文翻译：

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关于摩尔-彭罗斯逆是幂等的矩阵

摘要

本文研究了具有幂等摩尔-彭罗斯逆的方阵类。派生了该类的许多原始特征并确定了新属性。此外，散布在文献中的一些孤立的结果被重新捕获并以扩展或概括的形式重新推导。该研究受到一些矩阵方程（例如在物理学中出现）的启发，这些方程要么直接涉及具有幂等 Moore-Penrose 逆的矩阵，要么在所涉及的矩阵具有幂等 Moore-Penrose 逆的假设下其可解性提供了对相应的理论。