矩阵方程AX=B的正交(P,Q)-对称解

Orthogonal( P,Q)-symmetric solution of matrix equation AX = B

定义了正交(P,Q)-对称矩阵的概念,通过矩阵的正交投影构造了它的结构,针对正交(P,Q)-对称矩阵的正交不变性,采用直接代入法把问题转化为求矩阵方程组的正交解,利用矩阵的正交三角分解得出了矩阵方程组有正交(P,Q)-对称解的充分必要条件,及通解的表达式.最后得出矩阵方程AX=B有正交(P,Q)-对称解的充要条件及通解表达式.

Puts forward the concept of orthogonal （P,Q ）-symmetric matrix,and the structure was constructed through the orthogonal projection.According to the orthogonal invariance of orthogonal （P,Q）-symmetric matrix,The problem was converted to solve orthogonal solutions of matrix equations by adopting direct substitution method.Applying the orthogonal triangular decomposition for matrix ,necessary and sufficient conditions were derived and the general expression was gotten for the orthogonal solution to the matrix equations. The necessary and sufficient conditions were derived and the general expression was put forward for the orthogonal （P,Q）-symmetric solution to the matrix equation AX=B.