Download PDF - On melancholic magic squares
ArticleOriginal scientific text
Title
On melancholic magic squares
Authors 1, 2
Affiliations
- 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
Abstract
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.
Keywords
magic squares, patterns, group inverse, Moore-Penrose inverse, eigenvalues and eigenvectors
Bibliography
- W.S. Andrews, Magic Squares and Cubes (Dover, New York, 1960).
- A. Ben-Israel and T.N.E. Greville, Generalized Inverses: Theory and Applications (Springer, 2nd edition, 2003).
- H.D. Heinz and J.R. Hendricks, Magic Square Lexicon: Illustrated, HDH, Surrey, BC, 2000.
- 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.
- D. Trenkler and G. Trenkler, Magic squares, melancholy and the Moore-Penrose inverse, Image 27 (2001), 3-9.
Pages:
111-119
Main language of publication
English
Received
2013-04-12
Accepted
2013-10-26
Published
2013
DOI: 10.7151/dmps1155
Exact and natural sciences