奇数阶幻方的构造与特征值分析  

Construction of Odd Order Magic Squares and Its Eigenvalue Analysis

作　　者：刘乐乐[1] 

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《上海理工大学学报》2014年第1期1-4,共4页Journal of University of Shanghai For Science and Technology

摘　　要：对奇数阶幻方的一种构造方法进行改造,利用循环矩阵和对称循环矩阵的性质对奇数阶幻方的特征值进行分析,同时给出了奇数阶幻方全部特征值的统一计算公式,并最终否定了一些学者关于幻方特征值的猜测.The method for constructing odd order magic squares was reformed and the eigenvalues of odd order magic squares were analyzed based on the properties of circulant matrices and symmetric circulant matrices. Meanwhile, the unified calculation formula were given out. It is also found that some conjectures about the eigenvalues of magic squares are not correct.

关 键 词：幻方 循环矩阵 对称循环矩阵 特征值 

分 类 号：O151.2[理学—数学]