Normal magic square and its some matrix properties

Anup Kumar Thander; Chinmay Ghosh; Goutam Mandal

doi:https://doi.org/10.14445/22315373/IJMTT-V3I3P501

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 3 | Issue 3 | Year 2012 | Article Id. IJMTT-V3I3P501 | DOI : https://doi.org/10.14445/22315373/IJMTT-V3I3P501

Normal magic square and its some matrix properties

Anup Kumar Thander, Chinmay Ghosh, Goutam Mandal

Abstract

Some matrix properties on Eigen values, singular values, norm and condition number of normal magic square are presented in this paper. The properties are verified on a number of test examples and numerical results confirm that the properties are very effective for normal magic square. All the properties are checked using computational code in Matlab. In addition moment of inertia, surface plot and contour plot for different order normal magic squares are drawn.

Keywords

Eigen value, singular value, norm, conditional number, normal magic square.

References

[1]Cleve Moler, Chapter 10-Magic Squares, Math Works, Inc., 2011.
[2]Dianne Prost O’ Leary, Estimating matrix condition number, SIAM J. Sci. Stat. Comput, Vol. 1, No. 2, June 1980, 205-209. G. Abe, Unsolved Problems on Magic Squares, Disc. Math, 127(1994) 3-13.
[3]G. Abe, Unsolved Problems on Magic Squares, Disc. Math, 127(1994) 3-13
[4]K. Pinn, C. Wieczerkowski, Number of Magic Squares from Parallel Tempering Monte Carlo, Int. J. Mod. Phys, C 9, 1998, 541-547.
[5]Michael Y. Li and Liancheng Wang, A Criterion for Stability of Matrices, Journal of Mathematical Analysis & Applications, 225(1998), 249-264.
[6]Peter Loly, http://home.cc.umanitoba.ca/~loly/MathGaz.pdf

Citation :

Anup Kumar Thander, Chinmay Ghosh, Goutam Mandal, "Normal magic square and its some matrix properties," International Journal of Mathematics Trends and Technology (IJMTT), vol. 3, no. 3, pp. 91-94, 2012. Crossref, https://doi.org/10.14445/22315373/IJMTT-V3I3P501