矩阵方程的M-对称解

彭向阳;胡锡炎;张磊;

数学学报 ›› 2006, Vol. 49 ›› Issue (4) : 941-948.

数学学报 ›› 2006, Vol. 49 ›› Issue (4) : 941-948. DOI: 10.12386/A2006sxxb0116
论文

矩阵方程的M-对称解

    彭向阳;胡锡炎;张磊;
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The M-Symmetric Solutions of the Matrix Equation

    Xiang Yang PENGXi Yan HULei
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摘要

定义了M-对称矩阵集GSRn×n(M),获得了矩阵方程ATXA=B存在M-对称解的充分必要条件.解集为非空时,得到了最小范数解和给定矩阵X*最佳逼近解.

Abstract

This paper gives the definition of the set GSRn×n(M) and the necessary and sufficient conditions for the solvability of and the solution's general forms of ATXA= B. Let SE denote the set of solutions. Given an arbitrary X*,find a matrix X∈SE which is nearest to X* in Probenius norm. The matrix is unique and its expression is gives.

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最佳逼近解 / M-对称矩阵 / 矩阵方程

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彭向阳;胡锡炎;张磊;. 矩阵方程的M-对称解. 数学学报, 2006, 49(4): 941-948 https://doi.org/10.12386/A2006sxxb0116
Xiang Yang PENGXi Yan HULei. The M-Symmetric Solutions of the Matrix Equation. Acta Mathematica Sinica, Chinese Series, 2006, 49(4): 941-948 https://doi.org/10.12386/A2006sxxb0116

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