矩阵方程AXB=D的正交解
Orthogonal Solution of the Matrix Equation AXB=D
郭烨 1徐晶莹 1刘慧敏1
作者信息
- 1. 湖北师范大学文理学院理工学部,湖北 黄石 435109
- 折叠
摘要
利用矩阵的谱分解和奇异值分解,给出了矩阵方程AXB=D正交解存在的充要条件,且在正交解存在的条件下给出了正交解的表达式.除此之外,进一步讨论了最优逼近问题,导出了该矩阵方程最佳逼近正交解的表达式.最后通过数值实验验证了理论的正确性.
Abstract
In this paper,sufficient and necessary condition of existence of orthogonal solution for the matrix equation AXB=D is deduced by applying spectral and singular value decom-positions of matrices,and the expression of orthogonal solution to this matrix equation is also provided.Furthermore,the associated optimal approximate problem to the given matrix is discussed and the expression of optimal approximate orthogonal solution is derived.Finally,one numerical experiment is given to validate the correctness of the theories.
关键词
谱分解/奇异值分解/矩阵方程/正交解/最佳逼近Key words
spectral decomposition/singular value decomposition/matrix equation/orthog-onal solution/optimal approximation引用本文复制引用
出版年
2024
NETL
NSTL
万方数据