A construction of regular magic squares of odd order

被引：3

作者：

Chan, C. -Y. Jean ^{[1
]}

Mainkar, Meera G. ^{[1
]}

Narayan, Sivaram K. ^{[1
]}

Webster, Jordan D. ^{[2
]}

机构：

[1] Cent Michigan Univ, Mt Pleasant, MI 48859 USA

[2] Mid Michigan Community Coll, Harrison, MI 48625 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2014年 / 457卷

关键词：

Magic squares; Regular magic squares; Eigenvalues; Centroskew matrices; Circulant matrices;

D O I：

10.1016/j.laa.2014.05.032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A magic square is an n x n array of numbers whose rows, columns, and the two diagonals sum to mu. A regular magic square satisfies the condition that the entries symmetrically placed with respect to the center sum to 2 mu/n. Using circulant matrices we describe a construction of regular classical magic squares that are nonsingular for all odd orders. A similar construction is given that produces regular classical magic squares that are singular for odd composite orders. This paper is an extension of [3]. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：293 / 302

页数：10

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