摘要
在M.Newman研究矩阵的幂和问题的基础上,利用有限域中的方法,构造性地给出了有限域Fp上n次首一不可约多项式的次高项系数可以遍及Fp的一个有趣的引理,并由此证明有限域Fp上任一n×n矩阵均可表示成两个矩阵的p次幂之和.
On the basis of Newman's study on the powered sum of matrixes and with the method of finite field, an interesting lemma was constructively put forth that the factor of the term with n-1th power of a nth unreducible polynomial in finite field F_p can spread all over F_p, from which it was proved that any n×n matrix in F_p can be obtained by adding two matrixes raised to their pth power.
关键词
有限域
不可约多项式
极小多项式
标准有理块
finite field
unreducible polynomial
minimal polynomial
standard rational block
