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arXiv · 2007.02364

A new generalized inverse of matrices from core-EP decomposition

Kezheng Zuo·Yu Li·Gaojun Luo
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Abstract

A new generalized inverse for a square matrix $H\in\mathbb{C}^{n\times n}$, called CCE-inverse, is established by the core-EP decomposition and Moore-Penrose inverse $H^†$. We propose some characterizations of the CCE-inverse. Furthermore, two canonical forms of the CCE-inverse are presented. At last, we introduce the definitions of CCE-matrices and $k$-CCE matrices, and prove that CCE-matrices are the same as $i$-EP matrices studied by Wang and Liu in [The weak group matrix, Aequationes Mathematicae, 93(6): 1261-1273, 2019].

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Kezheng Zuo, Yu Li, Gaojun Luo. 2020-07-05. A new generalized inverse of matrices from core-EP decomposition. https://arxiv.org/abs/2007.02364

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