准幻方矩阵及其判定  

Quasi-Magic Square Matrix and Its Judgment

作　　者：刘玉[1] 郑晓周[1] 

机构地区：[1]韩山师范学院数学与信息技术系,广东潮州521041

出　　处：《南通大学学报（自然科学版）》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)

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.

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 

分 类 号：O151.21[理学—数学]