一定约束条件下矩阵方程AX=B的正交（P,Q）-反对称解

摘要

This paper presents the concept of orthogonal (P,Q)-skew symmetric matrix, and studies their structure .Applying the generalized orthogonal triangular decomposition for matrix , we derive necessary and sufficient conditions and the general expression for the orthogonal (P,Q)-skew symmetric solution to the matrix equation AX=B.%提出了正交(P,Q)-反对称矩阵的概念,对其结构进行了研究,并利用矩阵的正交三角分解研究矩阵方程AX =B有正交(P, Q)-反对称解的充分必要条件,及通解的表达式。