In this paper, we introduce a new generalized inverse, called weak core inverse (or, in short, WC inverse) of a complex square matrix. This new inverse extends the notion of the core inverse defined by Baksalary and Trenkler (Linear Multilinear Algebra 58(6):681–697, 2010). We investigate characterizations, representations, and properties for this generalized inverse. In addition, we introduce weak core matrices (or, in short, WC matrices) and we show that these matrices form a more general class than that given by the known weak group matrices, recently investigated by H. Wang and X. Liu.

中文翻译：

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弱芯逆

在本文中，我们介绍了一种新的广义逆，称为复方阵的弱核逆（或简称为WC逆）。这个新的逆扩展了Baksalary和Trenkler定义的核心逆的概念（线性多线性代数58（6）：681–697，2010）。我们研究此广义逆的特征，表示和性质。此外，我们介绍了弱核心矩阵（或简称为WC矩阵），并且我们证明这些矩阵比已知的弱群矩阵给出的类更通用，H。Wang和X. Liu最近对其进行了研究。