Polar and singular value decomposition of 3 x 3 magic squares

被引：0

作者：

Trenkler, Goetz ^{[1
]}

Schmidt, Karsten ^{[2
]}

Trenkler, Dietrich ^{[3
]}

机构：

[1] Dortmund Univ Technol, Fac Stat, D-44221 Dortmund, Germany

[2] Schmalkalden Univ Appl Sci, Fac Business & Econ, D-98574 Schmalkalden, Germany

[3] Univ Osnabruck, Dept Econ, D-49069 Osnabruck, Germany

来源：

INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY | 2013年 / 44卷 / 05期

关键词：

magic squares; polar decomposition; singular value decomposition; Luoshu;

D O I：

10.1080/0020739X.2013.790507

中图分类号：

G40 [教育学];

学科分类号：

040101 ; 120403 ;

摘要：

In this note, we find polar as well as singular value decompositions of a 3 x 3 magic square, i.e. a 3 x 3 matrix M with real elements where each row, column and diagonal adds up to the magic sum s of the magic square.

引用

页码：774 / 777

页数：6