摘要
本文研究了双随机循环矩阵中素元的分类问题.由于任一n阶双随机循环矩阵都可以唯一地表示为移位的n-1次一元多项式,从而可把双随机循环矩阵中素元的分类问题简化为解双随机循环矩阵上的一个方程.应用此原理,本文完全解决了判别具有位数3的n阶双随机循环矩阵是否为素元的问题,并给出了n阶双随机循环矩阵中一类具有位数4的素元.
The classification of primes in the doubly stochastic circulant matrices is now explored. Since any n x n doubly stochastic circulant matrix has a unique representation as a polynomial of degree n - 1 in the shift operator wn, the classification problem of primes in the doubly stochastic circulant matrices can be reduced to the solution of an equation over a doubly stochastic circulant matrix. By this means, the problem of deciding whether an n x n doubly stochastic circulant matrix A of order 3 is a prime is completely solved. A class of primes in the n × n doubly stochastic circulant matrices of order 4 is also presented.
出处
《数学学报(中文版)》
SCIE
CSCD
北大核心
2007年第3期661-668,共8页
Acta Mathematica Sinica:Chinese Series
基金
国家自然科学基金(10531080)
关键词
双随机循环矩阵
移位
素元
doubly stochastic circulant matrix
shift
prime matrix