2020/09/08 by R. P. Nordgren, Ronald P. Nordgren, Nordgren, Ronald P. · 1 citation
Computer Science · Mathematics · #Graph Labeling and Dimension Problems #math.GM #msc:15B99
paper · pdf · doi:10.48550/arxiv.2009.03499
18 pages, 3 examples. 2 commuting order-25 ultra magic square matrices in Ancillary File
arxiv created 2020/09/08 · arxiv updated 2020/09/09
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.