周富照.矩阵方程AXAT=C的对称斜反对称解[J].数学研究及应用,2005,25(2):292~298 |
矩阵方程AXAT=C的对称斜反对称解 |
Solutions of Matrix Equation AXAT = C in Symmetric and Skew-Antisymmetric Matrix Set |
投稿时间:2002-11-26 |
DOI:10.3770/j.issn:1000-341X.2005.02.011 |
中文关键词: 矩阵方程 对称斜反对称矩阵 广义奇异值分解 极小范数解 |
英文关键词:matrix equation symmetric and skew-antisymmetric matrix generalized singular-value decomposition minimal norm solution. |
基金项目:国家自然科学基金(50208004),中国博士后科学基金(2004036448),湖南省教育厅基金(04C099) |
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中文摘要: |
设A∈Rm×n,C∈Rm×m给定,利用矩阵的广义奇异值分解和对称斜反对称矩阵的性质,得到了矩阵方程(1)AXAT=C存在对称斜反对称解的充要条件和通解表达式;证明了若方程(1)有解,则一定存在唯一极小范数解,并给出了极小范数解的具体表达式和求解步骤. |
英文摘要: |
By applying the generalized singular-value decomposition (GSVD) of matrix pairs and the properties of symmetric and skew-antisymmetric , we obtain the sufficient and necessary conditions under which the matrix equation AXAT = C is solvable in n × n symmetric and skew-antisymmetric matrix set, and prove that if the above equation is solvable, then there exists a unique minimal norm solution, and give the procedure to find this solution, where A ∈ Rm×n and C ∈ Rm×m are given matrices. |
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