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矩阵方程$X^TAX=B$ 的反中心对称解

he Anti-centro-symmetric Solution of Matrix Equation $X^TAX=B$

中文摘要英文摘要

利用矩阵的广义奇异值分解,得到了线性矩阵方程$X^TAX=B$ 具有反中心对称解的充要条件, 得到了解的具体表达式;利用矩阵的标准相关分解给出了线性矩阵方程$X^TAX=B$ 在反中心对称矩阵集合上最小二乘解的通式; 另外,导出了在矩阵方程的解集合中与给定矩阵的最佳逼近解的表达式。

By applying the generalized singular value decomposition of matrices,this paper provides necessary and sufficient conditions for the existence and the expression of the anti-centro-symmetric solution of the linear matrix equation $X^TAX=B$.We also derive the expression of the equation.By applying the canonical correlation decomposition of matrix pairs,we obtain a general expression of the least-squares solution of the Matrix Equation $X^TAX=B$ in anti-centro-symmetric matrix set. In addition,we derive the expression of the optimal approximation expression in the solution set of corresponding equation.

肖庆丰、胡锡炎、张忠志

数学

矩阵方程反中心对称矩阵最小二乘解最佳逼近

matrix equationanti-centro-symmetric matrixleast-squares solutionoptimal approximation

肖庆丰,胡锡炎,张忠志.矩阵方程$X^TAX=B$ 的反中心对称解[EB/OL].(2006-01-23)[2025-08-18].http://www.paper.edu.cn/releasepaper/content/200601-275.点此复制

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