Commuting Magic Square Matrices
General Mathematics
2020-09-09 v1
Abstract
We review a known method of compounding two magic square matrices of order m and n with the all-ones matrix to form two magic square matrices of order mn. We show that these compounded matrices commute. Simple formulas are derived for their Jordan form and singular value decomposition. We verify that regular (associative) and pandiagonal commuting magic squares can be constructed by compounding. In a special case the compounded matrices are similar. Generalization of compounding to a wider class of commuting magic squares is considered. Three numerical examples illustrate our theoretical results.
Keywords
Cite
@article{arxiv.2009.03499,
title = {Commuting Magic Square Matrices},
author = {Ronald P. Nordgren},
journal= {arXiv preprint arXiv:2009.03499},
year = {2020}
}
Comments
18 pages, 3 examples. 2 commuting order-25 ultra magic square matrices in Ancillary File