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| 非负半环上强保持可逆矩阵的线性算子 | |
| 引用本文： | 李红海,谭宜家,唐加冕.非负半环上强保持可逆矩阵的线性算子[J].中国科学技术大学学报,2007,37(3):238-242. |
| 作者姓名： | 李红海 谭宜家 唐加冕 |
| 作者单位： | 1. 中国科学技术大学数学系,安徽合肥,230026 2. 福州大学数学系,福建福州,350002 3. 石家庄学院数学系,河北石家庄,050035 |
| 摘 要： | 设S是一非负交换半环,Mn(S)是S上所有矩阵构成的半环.对Mn(S)上一线性算子L,如果对任何A∈Mn(S),A可逆当且仅当L(A)可逆,则称L强保持Mn(S)中的可逆矩阵.刻画了在非负无零因子交换半环上强保持可逆矩阵的线性算子. |
| 关 键 词： | 非负交换半环 可逆矩阵 线性算子 |
| 文章编号： | 0253-2778(2007)03-0238-05 |
| 修稿时间： | 03 24 2005 12:00AM |
Linear operators that strongly preserve invertible matrices over antinegative semirings |
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| LI Hong-hai,TAN Yi-jia,TANG Jia-mian.Linear operators that strongly preserve invertible matrices over antinegative semirings[J].Journal of University of Science and Technology of China,2007,37(3):238-242. | |
| Authors: | LI Hong-hai TAN Yi-jia TANG Jia-mian |
| Institution: | 1. Department of Mathematics, University of Science and Technology of China, Hefei 230026, China 2. Department of Mathematics, Fuzhou University, Fuzhou 350002, China 3. Department of Mathematics, Shij iazhuang University, Shij iazhuang 050035, China |
| Abstract: | Let S be an antinegative commutative semiring and Mn(S) be the semiring of all n×n matrices over S. For a linear operator L on Mn (S), L strongly preserves invertible matrices in Mn(S) if for anyA∈Mn(S) A is invertible if and only if L(A) is invertible. The linear operators that strongly preserve invertible matrices over some antinegative commutative semirings with no zero divisors were characterized. |
| Keywords: | antinegative commutative semiring invertible matrix linear operator |
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