Abstract
Magic squares have been known in India from very early times. The renowned mathematician Ramanujan had immense contributions in the field of Magic Squares. A magic square is a square array of numbers where the rows, columns, diagonals and co-diagonals add up to the same number. The 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 matrix properties of 4×4 strongly magic squares dot products and different properties of eigen values and eigen vectors are discussed in detail.
Highlights
Magic squares date back in the first millennium B
A magic square of order n over a field where denotes the set of all real numbers is an nth order matrix [ ] with entries in such that
3.2.3. (1,1,1, ... .1)n is the eigen vector corresponding to the eigen value of a strongly magic square
Summary
Magic squares date back in the first millennium B. Magic squares generally fall into the realm of recreational mathematics [4, 5], a few times in the past century and more recently, they have become the interest of more-serious mathematicians. A normal magic square is a square array of consecutive numbers from 1 ... Where the rows, columns, diagonals and co-diagonals add up to the same number. Along with the conditions of normal magic squares, strongly magic square have a stronger property that the sum of the entries of the sub-squares taken without any gaps between the rows or columns is the magic constant [7]. There are many recreational aspects of strongly magic squares. Apart from the usual recreational aspects, it is found that these strongly magic squares possess advanced mathematical properties
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