| 矩阵空间上线性保持问题的几个结果 |
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| 引用本文： | 王艳涛,张显.矩阵空间上线性保持问题的几个结果[J].黑龙江大学自然科学学报,2009,26(5). |
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| 作者姓名： | 王艳涛 张显 |
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| 作者单位： | 黑龙江大学数学科学学院,哈尔滨,150080 |
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| 基金项目： | Supported by the Fund of Heilongjiang Education Committee for Overseas Scholars(1152HZ01);;the fund of Heilongjiang University for Younth Teachers(QLZ00501) |
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| 摘 要： | 设Mn(F)表示域F上所有n×n矩阵构成的线性空间,sln(F)表示Mn(F)的包含所有迹零矩阵的子空间。基于一些现有的结论,刻划了Mn(F)上可逆的线性秩1平方零(平方零、对合)保持,以及Mn(F)上强线性平方零(对合)保持,所获得的结果展示了几类线性保持问题间的关系。
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| 关 键 词： | 强线性对合保持 强线性平方零保持 线性秩1矩阵 线性秩1平方零保持 |
Several results on linear preserver problems on spaces of matrices |
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| WANG Yan-tao,ZHANG Xian.Several results on linear preserver problems on spaces of matrices[J].Journal of Natural Science of Heilongjiang University,2009,26(5). |
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| Authors: | WANG Yan-tao ZHANG Xian |
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| Institution: | School of Mathematics Science;Heilongjiang University;Harbin 150080;China |
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| Abstract: | Let M_n (F) be the linear space of all n×n matrices over a field F,and let sl_n (F) be the subspace of M_n (F) consisting of all zero-trace matrices.Based on some existing results,all invertible linear rank-1 square-zero (respectively,square-zero,involution) preservers on M_n (F) are characterized,and the structures of all strong linear square-zero (respectively,involution) preservers on M_n (F) are described.These results obtained here show clearly the relations among several linear preserver problems. |
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| Keywords: | (strong) linear involution preserver (strong) linear square-zero preserver linear rank-1 preserver linear rank-1 square-zero preserver |
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