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Dot Products and Matrix Properties of 4×4 Strongly Magic Squares
International Journal of Theoretical and Applied Mathematics
Volume 3, Issue 2, April 2017, Pages: 64-69
Received: Nov. 4, 2016; Accepted: Dec. 27, 2016; Published: Feb. 13, 2017
Authors
Neeradha. C. K., Dept. of Science & Humanities, Mar Baselios College of Engineering & Technology, Thiruvananthapuram, Kerala, India
V. Madhukar Mallayya, Department of Mathematics, Mohandas College of Engineering & Technology, Thiruvananthapuram, Kerala, India
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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.
Keywords
Strongly Magic Square (SMS), Dot Products of SMS, Eigen Values of SMS, Rank and Determinant of SMS
Neeradha. C. K., V. Madhukar Mallayya, Dot Products and Matrix Properties of 4×4 Strongly Magic Squares, International Journal of Theoretical and Applied Mathematics. Vol. 3, No. 2, 2017, pp. 64-69. doi: 10.11648/j.ijtam.20170302.13
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