Linear Algebraic Properties of Strongly Magic Squares

Abstract

Magic squares have turned up throughout history, some in a mathematical context, others in philosophical or religious contexts . They have always had a great influence upon mankind’s attitude. Although a definitive judgment of early history of magic squares is not available, it has been suggested that magic squares probably date back to India and pre-Islamic Persian origins. 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 subsquares 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, different properties of eigenvalues, and eigenvectors are discussed in detail.