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2013 | 33 | 1-2 | 111-119
Tytuł artykułu

On melancholic magic squares

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Starting with Dürer's magic square which appears in the well-known copper plate engraving Melencolia we consider the class of melancholic magic squares. Each member of this class exhibits the same 86 patterns of Dürer's magic square and is magic again. Special attention is paid to the eigenstructure of melancholic magic squares, their group inverse and their Moore-Penrose inverse. It is seen how the patterns of the original Dürer square to a large extent are passed down also to the inverses of the melancholic magic squares.
Twórcy
  • Dortmund University of Technology, Faculty of Statistics, Vogelpothsweg 87, D-44221 Dortmund, Germany
  • University of Osnabrück, Department of Economics, Rolandstraße 8, D-49069 Osnabrück, Germany
Bibliografia
  • [1] W.S. Andrews, Magic Squares and Cubes (Dover, New York, 1960).
  • [2] A. Ben-Israel and T.N.E. Greville, Generalized Inverses: Theory and Applications (Springer, 2nd edition, 2003).
  • [3] H.D. Heinz and J.R. Hendricks, Magic Square Lexicon: Illustrated, HDH, Surrey, BC, 2000.
  • [4] G.P.H. Styan, G. Trenkler and K.L. Chu, An Illustrated Introduction to Yantra Magic Squares and Agrippa-type Magic Squares, Lectures on Matrix and Graph Methods, Ed. by R.B. Bapat, S. Kirkland, U.M. Prasad and S. Puntanen (Manipal University Press, 2012), 159-220.
  • [5] D. Trenkler and G. Trenkler, Magic squares, melancholy and the Moore-Penrose inverse, Image 27 (2001), 3-9.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1155
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