广义主枢轴变换及其继承性质
Generalized Principal Pivot Transform and its Inheritance Properties
摘要：
本文给出了广义主枢轴变换的一些性质。给出了广义主枢轴变换的Moore-Penrose逆与其互补广义主枢轴变换的Moore-Penrose逆相等的充要条件。证明了广义主元变换保持给定方阵对称部分的秩。这些结果似乎比现有的更普遍。对于广义主元变换，还刻画了$P_{\dagger}$ -矩阵的继承性.
英文摘要：
In this paper, some more properties of the generalized principal pivot transform are derived. Necessary and sufficient conditions for the equality between Moore-Penrose inverse of a generalized principal pivot transform and its complementary generalized principal pivot transform are presented. It has been shown that the generalized principal pivot transform preserves the rank of symmetric part of a given square matrix. These results appear to be more generalized than the existing ones. Inheritance property of $P_{\dagger}$-matrix are also characterized for generalized principal pivot transform.
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