| 整数环上矩阵平方和的两个新结论 |
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| 引用本文： | 余览娒.整数环上矩阵平方和的两个新结论[J].数学的实践与认识,2001,31(5):579-591. |
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| 作者姓名： | 余览娒 |
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| 作者单位： | 温州师院数学系 |
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| 摘 要： | 本文利用 F2 上方阵为平方矩阵的充要条件 ,证明了 :1任一阶数为偶数的整数矩阵可表示成 5个平方次幂整数矩阵之和 ;2任一整数矩阵可表示成 6个平方次幂整数矩阵之和 ,从而改进了文 2 ,3 ]的主要结论 .
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| 关 键 词： | 平方次幂矩阵 不变因子 初等因子组 剩余类域 |
| 修稿时间： | 1998年9月3日 |
Two New Results of Sums of Square Matrices in Integer Ring |
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| YU Lan-mei.Two New Results of Sums of Square Matrices in Integer Ring[J].Mathematics in Practice and Theory,2001,31(5):579-591. |
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| Authors: | YU Lan-mei |
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| Abstract: | In this paper, by using the necessary and sufficient coindition of a square matrix in the fields of characteristic 2 we have proved the following results: 1) Every integer matrix which order is even number can be expressed as sums of 5 square integer matrices. 2) Every integer matrix of order n can be expressed as sums of 6 square integer matrices. The results of the article improve main results in . |
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| Keywords: | power matrix invariant factor elementary divisor residue class field |
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