Linear Transformation on Strongly Magic Squares
C. K. Neeradha., T. S. Sivakumar, V. Madhukar Mallayya · American journal of mathematics and statistics · 2017
A magic square is a square array of numbers where the rows, columns, diagonals and co-diagonals add up to the same number. Several studies on computational aspects of magic squares are being carried out recently revealing patterns, some of which have led to analytic insights, theorems or combinatorial results. Magic squares can be used for solving certain complicated and complex problems connected with the algebra and combinatorial geometry of polyhedra, polytopes. While magic squares are recreational on one hand they can be treated somewhat more seriously in higher mathematics on the other hand. This paper discuss about a well-known class of magic squares; the strongly magic square. The strongly magic square is a magic square with a stronger property that the sum of the entries of the sub-squares taken without any gaps between the rows or columns is also the magic constant. In this paper a generic definition for Strongly Magic Squares is given. The main objective of the paper is to define a function on strongly magic squares which can be established as a group homomorphism and isomorphism. The transition of a set of strongly magic squares to an abelian group can be seen in the paper. The paper deals with the formation of a vector space for the set of all strongly magic squares and particular types of strongly magic squares. The paper also sheds light on linear transformation on Strongly Magic Squares. The kernel of the mapping is also obtained.