In this paper, the concept of “Inverse Complemented Matrix Method”, introduced by Eagambaram (2018), has been reestablished with the help of minus partial order and several new properties of complementary matrices and the inverse of complemented matrix are discovered. Class of generalized inverses and outer inverses of given matrix are characterized by identifying appropriate inverse complement. Further, in continuation, we provide a condition equivalent to the regularity condition for a matrix to have unique shorted matrix in terms of inverse complemented matrix. Also, an expression for shorted matrix in terms of inverse complemented matrix is given.

中文翻译：

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矩阵的逆补和应用

在本文中，Eagambaram (2018) 引入的“逆补矩阵法”的概念在负偏序的帮助下重新建立，并发现了补矩阵和补矩阵的逆的几个新性质。给定矩阵的广义逆和外逆的类别通过识别适当的逆补来表征。此外，我们继续提供与正则性条件等价的条件，以使矩阵在逆补矩阵方面具有唯一的短矩阵。此外，还给出了用逆补矩阵表示的短矩阵。