摘要
给出了双心矩阵和双随机矩阵的一种推广矩阵——准幻方矩阵的定义,即设A∈Rn×n,如果A的每一行元素之和与每一列元素之和都为同一个常数,则称矩阵A为准幻方矩阵,得到了非负矩阵为准幻方矩阵的几个充要条件,并讨论了双心矩阵和双随机矩阵几个判定定理,得出了一些新的结果.
The definition of Quasi-magic square matrix, the generalized matrix of double heart matrix and doubly stochastic matrix, is tentatively presented. That is presuming A∈R^n×n, if added value of every line in A is the same constant, therefore matrix A is named Quasi-magic matrix. Several necessary and sufficient conditions for the non- negative matrix being quasi-magic square matrix are concluded, and at the same time several judgment theorems of the double heart matrices and doubly stochastic matrix are also discussed and new conclusions are drawn from them.
出处
《南通大学学报（自然科学版）》
CAS
2012年第4期86-89,共4页
Journal of Nantong University(Natural Science Edition)
基金
广东省自然科学基金项目(10152104101000008)
关键词
幻方矩阵
双心矩阵
双随机矩阵
准幻方矩阵
判定定理
magic square matrix
double heart matrix
doubly stochastic matrix
quasi-magic square matrix
judgment
