Abstract.

To extend the notation of inner inverses, we define weighted inner inverses of a rectangular matrix. In particular, we introduce a W -weighted (B, C)-inner inverse of A, for given matrices A, W, B, C, and present some characterizations and conditions for its existence. Since this new inverse is not unique, we describe the set of all W -weighted (B, C)-inner inverses of a given matrix. Several invertible matrix expressions which involve a W -weighted (B, C)-inner inverse of A are studied. Using such expressions, we represent a W -weighted (B, C)-inner inverse of some other matrix E. As a particular case of W -weighted (B, C)-inner inverse, we investigate (B, C)-inner inverses of a rectangular matrix. We also establish some reverse order law properties considering weighted inner inverses.

摘要。

为了扩展内部逆的符号，我们定义了矩形矩阵的加权内部逆。特别是，我们引入一个W¯¯加权（B，C）的σ-内部逆甲，对于给定的矩阵A，W，B，C，并给出其存在一些刻划和条件。由于此新逆不是唯一的，因此我们描述了给定矩阵的所有W加权（B，C）-内逆的集合。这涉及几个可逆矩阵表达式W¯¯加权（B，C）的σ-内部逆甲进行了研究。使用这样的表达式，我们表示W加权（B，C）-其他矩阵E的内部逆。作为W加权（B，C）-内部逆的一种特殊情况，我们研究了矩形矩阵的（B，C）-内部逆。我们还考虑了加权内部逆，建​​立了一些逆序定律性质。