| Rn上的投影阵与不相容线性方程组的最优解 |
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| 引用本文： | 郭华.Rn上的投影阵与不相容线性方程组的最优解[J].重庆工商大学学报(自然科学版),2002,19(1):14-17. |
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| 作者姓名： | 郭华 |
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| 作者单位： | 渝州大学数学与计算机科学系,重庆,400033 |
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| 摘 要： | 研究了所有n维实向量构成的线性空间Rn上的投影阵 ,从线性变换的角度给出了投影阵定义 ,讨论了其性质 ,指出了Rn上一般投影阵与P=A(ATA) 1 AT 之间的关系 ,以及与不相容性方程组的最优解之间的紧密联系。
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| 关 键 词： | 投影阵 投影变换 投影向量 实幂等矩阵 列空间 核空间 不相容线性方程组 |
| 文章编号： | 1006-3293(2002)01-0014-04 |
| 修稿时间： | 2001年12月11 |
Projection Matrix on Rn and the Optimal Solution of Inconsistent Linear Simultaneous Equations |
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| GUO Hua.Projection Matrix on Rn and the Optimal Solution of Inconsistent Linear Simultaneous Equations[J].Journal of Chongqing Technology and Business University:Natural Science Edition,2002,19(1):14-17. |
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| Authors: | GUO Hua |
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| Abstract: | The projection matrixes on linear space R n composed of all n_dimension real vectors was studied. The definition of projection matrix was given with the view of linear transform,and its properties were also discussed. Furthermore,the realtions between general projection matrix and P=A TA) -1 A T on R n ,and between that and the optimal solution of inconsistent linear simultaneous equations were pointed out. |
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| Keywords: | projection matrix projection transform projection rector real idempotent matrix column space nuclear space inconsistent linear simultaneous equations |
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