A construction of regular magic squares of odd order

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Abstract

A magic square is an n×n array of numbers whose rows, columns, and the two diagonals sum to μ. A regular magic square satisfies the condition that the entries symmetrically placed with respect to the center sum to 2μn. Using circulant matrices we describe a construction of regular classical magic squares that are nonsingular for all odd orders. A similar construction is given that produces regular classical magic squares that are singular for odd composite orders. This paper is an extension of [3].

Original languageEnglish
Pages (from-to)293-302
Number of pages10
JournalLinear Algebra and Its Applications
Volume457
DOIs
StatePublished - Sep 15 2014

Keywords

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

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