| 矩阵方程的AXB＋CYD=E反对称极小范数最小二乘解 |
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| 引用本文： | 李水勤,邓继恩.矩阵方程的AXB＋CYD=E反对称极小范数最小二乘解[J].南阳理工学院学报,2010,2(2):95-98. |
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| 作者姓名： | 李水勤 邓继恩 |
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| 作者单位： | 河南理工大学数学与信息科学院,河南,焦作,454003 |
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| 摘 要： | 对任意给定的矩阵A∈R^m×n，B∈n×s，C∈R^m×k，D∈R^k×s，E∈R^m×s，本文利用矩阵的拉直算子，Moore—Penrose（M—P）广义逆及Kronecker积，研究矩阵方程AXB＋CYD=E的反对称最小二乘解，给出了解的表达式。并由此给出了该方程的反对称极小范数最小二乘解的表达式，同时给出了该方程有反对称解的充分必要条件及反对称解的表达式。
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| 关 键 词： | 反对称矩阵 极小范数解 最小二乘解 Moore—Penrose广义逆 Kronecker积 |
LEAST SQUARES ANTI-SYMMETRIC SOLUTION OF THE MATRIX EQUATION AXB+CYD=E WITH THE LEAST NORM |
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| LI Shui-qin,DENG Ji-en.LEAST SQUARES ANTI-SYMMETRIC SOLUTION OF THE MATRIX EQUATION AXB+CYD=E WITH THE LEAST NORM[J].Journal of Nanyang Institute of Technology,2010,2(2):95-98. |
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| Authors: | LI Shui-qin DENG Ji-en |
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| Institution: | ( School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 45003, China ) |
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| Abstract: | Given matrices A∈R^m×n,B∈n×s,C∈R^m×k,D∈R^k×s,E∈R^m×s, the least-squares anti-symmetric solution of the matrix equation AXB ＋ CYD = E is studied by using Moore-Penrose generalized inverse and Kronecker product, and its expression is given in this article. Based on this, the expression of the least-squares anti-symmetric solution is deprived with the least norm, the necessary and sufficient conditions for the existence of the anti-symmetric solution and its expression are also presented. |
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| Keywords: | Anti-symmetric matrix Least norm solution Moore-Penrose generalized inverse Kronecker product Least-squares solution |
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