| 一类四元数矩阵方程的最小二乘解 |
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| 引用本文： | 徐清舟,张志立. 一类四元数矩阵方程的最小二乘解[J]. 郑州大学学报(理学版), 2005, 37(1): 13-15,20 |
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| 作者姓名： | 徐清舟 张志立 |
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| 作者单位： | 1. 许昌学院数学系,河南,许昌,461000
2. 许昌学院网络中心,河南,许昌,461000 |
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| 摘 要： | 利用广义自反矩阵和广义反自反矩阵的性质讨论了线性方程组AX=b和矩阵方程AX=B的最小二乘解问题.当A为广义自反矩阵或广义反自反矩阵时,可将线性方程组AX=b的最小二乘解问题化为两个较小独立的子问题;当A、B都是广义自反矩阵或广义反自反矩阵时,可将矩阵方程AX=B的最小二乘解问题化为线性方程组的最小二乘解问题,从而使这些问题的讨论得到简化.
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| 关 键 词： | 四元数体 矩阵方程 最小二乘解 |
| 文章编号： | 1671-6841(2005)01-0013-03 |
Least Squares Solutions of Matrix Equations over Quaternion Field |
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| Xu Qingzhou,Zhang Zhili. Least Squares Solutions of Matrix Equations over Quaternion Field[J]. Journal of Zhengzhou University(Natrual Science Edition), 2005, 37(1): 13-15,20 |
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| Authors: | Xu Qingzhou Zhang Zhili |
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| Abstract: | By using of the properties of the generalization reflexive (antireflexive) matrices,the problems are discussed that least squares solutions of systems of linear equation AX=b and matrices equation AX=B.When A is the generalization reflexive (antireflexive) matrices, least squares problems of systems of linear equation AX=b can be decomposed into two smaller and independent subproblems.When A,B both are the generalization reflexive(antirefiexive) matrices, least squares problems of matrix equation AX=B can be decomposed into least squares problems of systems of linear equation.By this way, the discussion of these problems can be simplified. |
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| Keywords: | quaternion field matrix equations least squares solution |
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