摘要
本文主要研究定义在二元有限域GF(2)上友矩阵的性质,文中采用对矩阵性质的一般研究方法,较系统地讨论了定义在二元有限域上友矩阵的行列式、可逆性、特征值、秩、对角化以及极小多项式等有关问题,并得到了一些相关结论。
This article discusses the properties of companion matrix over binary field.It consults the general methods on the discussion about matrix property to discuss the properties of companion matrix such as determinant,invertibility, characteristic value, rank, diagonalizable, minimal polynomial and other problems and we obtains some main conclusions.
关键词
二元有限域
友矩阵
可逆性
秩
对角化
极小多项式
binary field
companion matrix
invertible
rank
diagonalizable
minimal polynomial
