有限域F_2上平方矩阵问题的讨论

Discussion on the problem of Square Matrix over Finite Field F_2

在特征为2的域F2上给出n阶矩阵为平方矩阵的充要条件,从而刻划了平方矩阵的特征,求出环Fq[x]上有限生成模的自同构群的阶数公式,由此得到F2上全体平方矩阵的计数公式.

In this paper, a necessary and sufficient condition for matrices of order n to be square matrix is given, with which the characterizations on square matrix are obtained. Meanwhile, the formula about number of order on the group of automorphisms over finitely generated module over Ring Fq [ x ] is deduced. So enumeration formula of all the square matrices over finite field F2 is established.