| 四元数矩阵方程AXAH=B的最小二乘解 |
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| 引用本文： | 刘永辉.四元数矩阵方程AXAH=B的最小二乘解[J].数学研究,2003,36(2):145-150. |
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| 作者姓名： | 刘永辉 |
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| 作者单位： | 华东师范大学数学系,上海,200062;枣庄师范专科学校数学系,山东,枣庄,277160 |
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| 基金项目： | ThisauthorwassupportedbyShanghaiPriorityAcademicDisciplineFoundation ,Shanghai,China |
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| 摘 要： | 引入了四元数矩阵范数的概念，通过使用四无数矩阵的奇异值分解，给出了四元数矩阵方程AXA^H＝B在最小二乘意义下的Hermitian解以及Skew-Hermitian解．
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| 关 键 词： | 四元数矩阵方程 最小二乘解 Hermitian解 奇异值分解 |
The Least-square Solutions to the Quaternion matrix Equation AXAH=B |
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| Liu Yonghui.The Least-square Solutions to the Quaternion matrix Equation AXAH=B[J].Journal of Mathematical Study,2003,36(2):145-150. |
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| Authors: | Liu Yonghui |
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| Abstract: | In this paper, the norms of quaternion matrices are introduced. By applying the singular value decomposition on quaternion matrices, we obtain the general expression of the least-square solutions of the matrix equation AXAH=B under the restriction that the solution matrix X∈Qn×n is Hermitian (or Skew-Hermitian), where A∈Qm×n and B∈Qm×m are given matrices. |
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| Keywords: | quaternion matrix equation hermitian solution least-square solution singular-value decomposition |
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