主枢轴变换：性质和应用
Principal pivot transforms: properties and applications
摘要：
一个矩阵A相对于一个可逆的前导主子矩阵的主枢轴变换（PPT）是一个矩阵B，使得A [x_1^T x_2^T]^T = [y_1^T y_2^T]^T当且仅当B [y_1^T x_2^T]^T = [x_1^T y_2^T]^T，其中所有向量共形地划分到A。本文的目的是综述与任意主子阵相关的PPT的性质和表现形式，提出一些新的观察结果，展示PPT在矩阵理论中的进一步应用。我们特别注意主子式为正的矩阵的PPT。
英文摘要：
The principal pivot transform (PPT) of a matrix A partitioned relative to an invertible leading principal submatrix is a matrix B such that A [x_1^T x_2^T]^T = [y_1^T y_2^T]^T if and only if B [y_1^T x_2^T]^T = [x_1^T y_2^T]^T, where all vectors are partitioned conformally to A. The purpose of this paper is to survey the properties and manifestations of PPTs relative to arbitrary principal submatrices, make some new observations, present and possibly motivate further applications of PPTs in matrix theory. We pay special attention to PPTs of matrices whose principal minors are positive.
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