| 可换矩阵空间的最大维数 |
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| 引用本文： | 唐建国,TANG Jian-guo.可换矩阵空间的最大维数[J].上海大学学报(英文版),2000,4(3):186-193. |
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| 作者姓名： | 唐建国 TANG Jian-guo |
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| 作者单位： | TANG Jianguo 1，2 1. College of Sciences，Shanghai University，Shanghai 200436，China 2. Department of Mathematics，Lingling Teachers College，Yongzhou，Hunan 425006，China |
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| 基金项目： | Supported by the Youth Mainstay Teacher Foundation of Hunan
Province Educational Committee |
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| 摘 要： | Ｄｅｆｉｎｉｔｉｏｎ ＬｅｔＷｂｅａｓｕｂｓｐａｃｅｏｆＭｎ(Ｃ) ,ｔｈｅｎ ｏｒｄｅｒｍａｔｒｉｘｓｐａｃｅｏｎｃｏｍｐｌｅｘｆｉｅｌｄ .ＩｆＡＢ =ＢＡ , Ａ ,Ｂ∈Ｗ ,ｔｈｅｎＷｉｓｃａｌｌｅｄａｃｏｍｍｕｔａｂｌｅｍａｔｒｉｘｓｐａｃｅ(ＣＭＳ)ｏｆＭｎ(Ｃ) . ＡｍｏｎｇａｌｌＣＭＳｏｆＭｎ(Ｃ) ,ｔｈｅｒｅｍｕｓｔｅｘｉｓｔａＣＭＳｗｉｔｈｍａｘｉｍａｌｄｉｍｅｎｓｉｏｎｓ,ｄｅｎｏｔｅｄｂｙＷ(ｎ)ｍａｘ,ａｎｄｔｈｅｍａｘｉｍａｌｄｉｍｅｎｓｉｏｎｓｂｙｄ(ｎ)ｍａｘ.Ｔｈｅｃｏｎｓｔｒｕｃｔｉｏｎ…
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| 收稿时间： | 27 September 1999 |
Estimation of maximal dimensions of commutable matrix spaces |
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| Jian-guo Tang.Estimation of maximal dimensions of commutable matrix spaces[J].Journal of Shanghai University(English Edition),2000,4(3):186-193. |
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| Authors: | Jian-guo Tang |
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| Institution: | College of Sciences, Shanghai University, Shanghai 200436, China;Department of Mathematics, Lingling Teachers College, Yongzhou , Hunan 425006, China |
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| Abstract: | In this paper, a lower bound of maximal dimensions of commutable matrix spaces (CMS) is given. It is found that the linear dependence of a group of one to one commutable matrices is related to whether some equations in system can be eliminated. The corresponding relation is given. By introducing conceptions of eliminating set and eliminating index, we give an estimation of upper bound of maximal dimensions of CMS. For special cases n=5,6, the further estimation of maximal dimensions of CMS is presented. |
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| Keywords: | commutable matrix space maximal dimension linear dependence Jordan block order little block |
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