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International Journal of Mathematics and Mathematical Sciences
Volume 2016, Article ID 9721725, 7 pages
http://dx.doi.org/10.1155/2016/9721725
Research Article

Vector Spaces of New Special Magic Squares: Reflective Magic Squares, Corner Magic Squares, and Skew-Regular Magic Squares

Department of Mathematics, Faculty of Science, Srinakharinwirot University, Bangkok 10110, Thailand

Received 13 September 2016; Accepted 3 November 2016

Academic Editor: Marianna A. Shubov

Copyright © 2016 Thitarie Rungratgasame et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The definition of a regular magic square motivates us to introduce the new special magic squares, which are reflective magic squares, corner magic squares, and skew-regular magic squares. Combining the concepts of magic squares and linear algebra, we consider a magic square as a matrix and find the dimensions of the vector spaces of these magic squares under the standard addition and scalar multiplication of matrices by using the rank-nullity theorem.