On nonsingular regular magic squares of odd order

Michael Z. Lee, Elizabeth Love, Sivaram K. Narayan, Elizabeth Wascher, Jordan D. Webster

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Using centroskew matrices, we provide a necessary and sufficient condition for a regular magic square to be nonsingular. Using latin squares and circulant matrices we describe a method of construction of nonsingular regular magic squares of order n where n is an odd prime power.

Original languageEnglish
Pages (from-to)1346-1355
Number of pages10
JournalLinear Algebra and Its Applications
Issue number6
StatePublished - Sep 15 2012


  • Centroskew matrices
  • Circulant matrices
  • Eigenvalues
  • Latin squares
  • Magic squares
  • Regular magic squares


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