| 一类四元数矩阵方程的反中心对称解及其最佳逼近 |
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| 引用本文： | 于艳,黄敬频. 一类四元数矩阵方程的反中心对称解及其最佳逼近[J]. 广西科学院学报, 2008, 24(2): 79-83 |
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| 作者姓名： | 于艳 黄敬频 |
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| 作者单位： | 广西民族大学数学与计算机科学学院,广西南宁,530006;广西民族大学数学与计算机科学学院,广西南宁,530006 |
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| 基金项目： | 广西自然科学基金 , 广西教育厅科研项目 |
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| 摘 要： | 利用四元数矩阵对的广义奇异值分解,讨论四元数矩阵方程AXB=C具有反中心对称解的充要条件,得到解的具体表达式,并应用Frobenius范数酉不变性,在该方程的反中心对称解集合中导出与给定相同类型矩阵的最佳逼近解的表达式.
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| 关 键 词： | 四元数矩阵方程 广义奇异值分解 Frobenius范数 反中心对称矩阵 最佳逼近 |
| 收稿时间： | 2007-10-30 |
Anti-centrosymmetric Solutions for Quaternion Matrices Equations and Its Optimal Approximation |
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| YU Yan and HUANG Jing-pin. Anti-centrosymmetric Solutions for Quaternion Matrices Equations and Its Optimal Approximation[J]. Journal of Guangxi Academy of Sciences, 2008, 24(2): 79-83 |
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| Authors: | YU Yan and HUANG Jing-pin |
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| Affiliation: | YU Yan,HUANG Jing-pin(College of Mathematics , Computer Science,Guangxi University for Nationalities,Nanning,Guangxi,530006,China) |
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| Abstract: | By using generalized singular value decomposition of quaternion matrices,the necessary and sufficient conditions of the quaternion matrix equation AXB=C having the anti-centro-symmetry solutions are discussed,and the specific expression of the solution is obtained.Meanwhile,by using unitary invariant property of Frobenius norm,the expression of the best approximation solution corresponding with given type of matrices are derived from the anti-centro-symmetry solutions set of this quaternion matrix equation. |
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| Keywords: | quaternion matrix equation generalized singular value decomposition Frobenius norm anti-centro-symmetry matrix best approximation |
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