| 引用本文： |
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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. [点击复制]
- YU Yan,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. [点击复制]
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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. |
| 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 |
| DOI： |
| 投稿时间：2007-10-30 |
| 基金项目:广西自然科学基金项目(2008J32),广西教育厅科研基金项目(2006J26)资助。 |
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| Anti-centrosymmetric Solutions for Quaternion Matrices Equations and Its Optimal Approximation |
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YU Yan, HUANG Jing-pin
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| (College of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, Guangxi, 530006, China) |
| 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. |
| Key words: quaternion matrix equation generalized singular value decomposition Frobenius norm anti-centro-symmetry matrix best approximation |
