| 关于与给定矩阵可交换的矩阵的多项式表示 |
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| 引用本文： | 杨忠鹏,冯晓霞,张清新. 关于与给定矩阵可交换的矩阵的多项式表示[J]. 大学数学, 2012, 0(1): 99-106 |
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| 作者姓名： | 杨忠鹏 冯晓霞 张清新 |
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| 作者单位： | 莆田学院数学系;漳州师范学院数学系 |
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| 基金项目： | 福建省自然科学基金项目(2010J01018);2008年福建省高校服务海西建设重点项目(2008HX03);福建省教育厅科技项目(JA08196,JA09167) |
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| 摘 要： | 文[1]得到:若矩阵A的Jordan标准形中没有纯量矩阵的Jordan块,那么AB=BA的充要条件为B可以化为A的n-1次多项式.本文指出这个结论是错误的.在已有相关文献的基础上,得到了与给定矩阵A可交换的矩阵B是A的多项式的十个等价刻划.
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| 关 键 词： | 可交换矩阵 多项式矩阵 非减次矩阵 Jordan标准形 最小多项式 |
The Polynomial Denotation for the Matrix Being Changeable with a Given Matrix |
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| YANGZhong-peng,FENG Xiao-xia,ZHANG Qing-xin. The Polynomial Denotation for the Matrix Being Changeable with a Given Matrix[J]. College Mathematics, 2012, 0(1): 99-106 |
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| Authors: | YANGZhong-peng FENG Xiao-xia ZHANG Qing-xin |
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| Affiliation: | 1,2 (1.Department of Mathematics,Putian University,Putian,Fujian 351100,China; 2.Department of Mathematics,Zhangzhou Normal University,zhangzhou,Fujian363000,China) |
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| Abstract: | [1] obtained: if there is not the Jordan block corresponding to the scalar matrix in the Jordan canonical form of the matrix A,then the necessary and sufficient condition of AB=BA is that B can be n-1-order polynomial about A.In the paper,we pointed the conclusion is wrong.On the basis of the previously related literatures,we derive ten equivalent characterizations that the matrix B being changeable with given matrix A is the polynomial about A. |
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| Keywords: | changeable matrix polynomial matrix non-derogatory matrix Jordan canonical form minimal polynomial |
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