有限数域上的矩阵结构(续)

本文把前文中关于非奇矩阵的某次乘幂在质数基的有限数域中恰好是一个单位矩阵的事实推广到奇异矩阵的情况上去,证明了在有限数域上的奇异矩阵乘幂中有准循环性存在,并且应用这些性质寻找一种解方程组的精确算法,包括相容方程组在内,也同时解决了偶然发生的奇异化现象所带来的困难。

The Construction of Matrices of Finite Number Field (Continuation)

In this article, the author expands the fact that a specific power of a nonsingular matrix is a unit matrix in a finite field based on a prime number, presented previously in the same named paper, into the singular situation, and proves that there is a subperiodic structure about a singular matrix in a finite field. An attempt is made to apply these characters to find out an accurate solution to indeterminate equations of linear algebra. These efforts prove to have the effect of solving the singularization occasionally occured in mapping from real number field into finite field, and provide an exact method for adoption in some problems of numerical calculation.