| 交换环上的复合伴随矩阵 |
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| 引用本文： | 王莹,郑宝东.交换环上的复合伴随矩阵[J].黑龙江大学自然科学学报,2005,22(1):113-116. |
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| 作者姓名： | 王莹 郑宝东 |
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| 作者单位： | 哈尔滨工业大学,理学院,黑龙江,哈尔滨,150001;哈尔滨工业大学,理学院,黑龙江,哈尔滨,150001 |
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| 摘 要： | 研究交换环上复合伴随矩阵的性质, 证明交换环上幂等 (幂零,幂单 )矩阵的复合伴随矩阵还是幂等(幂零,幂单)矩阵, 讨论交换环上复合伴随矩阵的Smith标准形,建立交换环上矩阵A的秩与A的复合伴随矩阵C*k (A)的秩之间的关系.
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| 关 键 词： | 复合伴随矩阵 幂等(幂零 幂单)矩阵 Smith标准形 |
| 文章编号： | 1001-7011(2005)01-0113-04 |
| 修稿时间： | 2003年10月15 |
Compound adjoint matrices over commutative rings |
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| WANG Ying,ZHENG Bao-dong.Compound adjoint matrices over commutative rings[J].Journal of Natural Science of Heilongjiang University,2005,22(1):113-116. |
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| Authors: | WANG Ying ZHENG Bao-dong |
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| Abstract: | Some properties of compound adjoint matrices over commutative rings are considered. It is proved that the compound adjoint matrix of an idempotent (nilpotent, unipotent) matrix over commutative rings is idempotent (nilpotent, unipotent). Smith normal forms of compound adjoint matrices over any commutative ring are discussed. The relation between the rank of a matrix and the rank of its compound adjoint matrix over any commutative ring is given. |
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| Keywords: | compound adjoint matrix idempotent matrix nilpotent matrix unipotent matrix Smith normal form |
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