| I{2}和M{2}的有效刻画(英文) |
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| 引用本文： | 征道生.I{2}和M{2}的有效刻画(英文)[J].华东师范大学学报(自然科学版),2015,2015(1):42-50. |
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| 作者姓名： | 征道生 |
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| 作者单位： | 华东师范大学数学系, 上海 200241 |
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| 摘 要： | Stewart给出了一个矩阵2-逆集合M{2}的刻画公式.但其中含有多余的任意参数,因而不是一个有效刻画.本文利用方阵的满秩分解,为I{2}_s的一个真子集B_1剔除了Stewart公式中的多余任意参数,得到了B_1的有效刻画公式;还证明了I{2}是其有限个子集的并集,其中每个子集与B_1等距同构.由此可分别建立I{2},I{2},M{2}和M{2}的有效刻画公式.算法2.1则可用于无重复地计算I{2}_s的每个元素.
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| 关 键 词： | 广义逆矩阵类的有效刻画 两个集合的2-范等距同构 矩阵的满秩分解 矩阵方程的解 |
| 收稿时间： | 2013-10-01 |
Efficient characterization for I{2} and M{2} |
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| ZHENG Dao-sheng.Efficient characterization for I{2} and M{2}[J].Journal of East China Normal University(Natural Science),2015,2015(1):42-50. |
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| Authors: | ZHENG Dao-sheng |
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| Institution: | ZHENG Dao-sheng;Department of Mathematics,East China Normal University; |
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| Abstract: | An important characterization formula for M{2} was given by Stewart where M 2 Cm×n. But this formula contains redundant arbitrary parameters, and therefore is nonefficient. This paper, by using the matrix full rank decomposition, showed that for a proper subset of I{2}s, which is denoted as B1, the redundant arbitrary parameters in Stewart’s formula can be eliminated, and I{2}s is a union set of its certain subsets, and each of the subsets is 2-norm isometry with B1. Finally, the efficient characterization fonmulas for I{2}s, I{2} and M{2} are obtained respectively. An algorithm was provided that can be used to compute any element of I{2}s, and avoid the repeat computation work for each
element of I{2}s. |
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| Keywords: | efficient characterization for a generalized inverse matrix set 2-norm isometry of two sets matrix full-rank factorization solution set of a matrix equation |
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