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.
| Published in | International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 2) |
| DOI | 10.11648/j.ijtam.20170302.13 |
| Page(s) | 64-69 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Strongly Magic Square (SMS), Dot Products of SMS, Eigen Values of SMS, Rank and Determinant of SMS
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| [5] | C. Pickover. The Zen of Magic Squares, Circles and Stars. Princeton University Press, Princeton, NJ, 2002. |
| [6] | Bruce C. Berndt, Ramanujan’s Notebooks Part I, Chapter 1 (pp 16-24), Springer, 1985. |
| [7] | T. V. Padmakumar “Strongly Magic Square”, Applications Of Fibonacci Numbers Volume 6 Proceedings of The Sixth International Research Conference on Fibonacci Numbers and Their Applications, April 1995. |
| [8] | Charles Small, “Magic Squares Over Fields” The American Mathematical Monthly Vol. 95, No. 7 (Aug. - Sep., 1988), pp. 621-625. |
| [9] | Neeradha. C. K, Dr. V. Madhukar Mallayya “Generalized Form Of A 4x4 Strongly Magic Square” IJMMS, Vol. 12, No. 1 (January-June; 2016), pp 79-84. |
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APA Style
Neeradha. C. K., V. Madhukar Mallayya. (2017). Dot Products and Matrix Properties of 4×4 Strongly Magic Squares. International Journal of Theoretical and Applied Mathematics, 3(2), 64-69. https://doi.org/10.11648/j.ijtam.20170302.13
ACS Style
Neeradha. C. K.; V. Madhukar Mallayya. Dot Products and Matrix Properties of 4×4 Strongly Magic Squares. Int. J. Theor. Appl. Math. 2017, 3(2), 64-69. doi: 10.11648/j.ijtam.20170302.13
AMA Style
Neeradha. C. K., V. Madhukar Mallayya. Dot Products and Matrix Properties of 4×4 Strongly Magic Squares. Int J Theor Appl Math. 2017;3(2):64-69. doi: 10.11648/j.ijtam.20170302.13
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Download@article{10.11648/j.ijtam.20170302.13,
author = {Neeradha. C. K. and V. Madhukar Mallayya},
title = {Dot Products and Matrix Properties of 4×4 Strongly Magic Squares},
journal = {International Journal of Theoretical and Applied Mathematics},
volume = {3},
number = {2},
pages = {64-69},
doi = {10.11648/j.ijtam.20170302.13},
url = {https://doi.org/10.11648/j.ijtam.20170302.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170302.13},
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.},
year = {2017}
}
TY - JOUR T1 - Dot Products and Matrix Properties of 4×4 Strongly Magic Squares AU - Neeradha. C. K. AU - V. Madhukar Mallayya Y1 - 2017/02/13 PY - 2017 N1 - https://doi.org/10.11648/j.ijtam.20170302.13 DO - 10.11648/j.ijtam.20170302.13 T2 - International Journal of Theoretical and Applied Mathematics JF - International Journal of Theoretical and Applied Mathematics JO - International Journal of Theoretical and Applied Mathematics SP - 64 EP - 69 PB - Science Publishing Group SN - 2575-5080 UR - https://doi.org/10.11648/j.ijtam.20170302.13 AB - 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. VL - 3 IS - 2 ER -
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