A new decomposition for square matrices is constructed by using two known matrix decompositions. A new characterization of the core-EP order is obtained by using this new matrix decomposition. We also use this matrix decomposition to investigate the minus, star, sharp and core partial orders in the setting of complex matrices.

中文翻译：

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基于 CS 分解的偏序

通过使用两个已知的矩阵分解构造了一种新的方阵分解。通过使用这种新的矩阵分解，可以获得核心-EP 顺序的新特征。我们还使用这种矩阵分解来研究复杂矩阵设置中的负偏序、星形偏序、尖锐偏序和核心偏序。