Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-28T13:31:18.770Z Has data issue: false hasContentIssue false

Latin square matrices and their inverses

Published online by Cambridge University Press:  06 June 2019

K. Robin McLean*
Affiliation:
Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL e-mail: [email protected]

Extract

Magic squares have long been popular in recreational mathematics. Their potential for introducing students to ideas in linear algebra was recognised over forty years ago in [1] and later in [2]. More recently they have proved to be a fascinating topic for undergraduate exploration, especially when students have access to a computer algebra package [3]. Some results on powers of magic square matrices can be found in [4], [5] and [6]. (Readers who google the title ‘Odd magic powers’ of Thompson’s paper [5] will be treated to a wide variety of non-mathematical exotica!)

Type
Articles
Copyright
© Mathematical Association 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Fletcher, T. J., Linear algebra through its applications, Van Nostrand Reinhold, New York (1972).Google Scholar
Van den Essen, A., Magic squares and linear algebra, American Math. Monthly 97 (1990) pp. 60-62.10.1080/00029890.1990.11995550CrossRefGoogle Scholar
Pountney, D. C., Magic squares and DERIVE, Fourth International Derive TI-89/92 Conference, Liverpool John Moores University, July 12-15, 2000, accessible at http://rfdz.ph-noe.ac.at/fileadmin/Mathematik_Uploads/ACDCA/Liverpool2000/pdf/Papers/Pountney.pdfGoogle Scholar
Hill, R. and Elzaidi, S. M., Cubes and inverses of magic squares, Math. Gaz. 80 (November 1996) pp. 565-567.10.1017/S0025557200185845CrossRefGoogle Scholar
Thompson, A. C., Odd magic powers, American Math. Monthly 101 (1994) pp. 339-342.Google Scholar
Cook, C. K., Bacon, M. R. and Hillman, R.A., The ‘magicness’ of some magic squares, The Fibonacci Quarterly 48 (2010) pp. 298-306.Google Scholar
Fisher, R. A., The design of experiments, Oliver & Boyd, Edinburgh (1935).Google Scholar
Dénes, J. and Keedwell, A., Latin squares and their applications, Academic Press, New York (1974); 2nd edition, North Holland, Elsevier, Amsterdam (2015).Google Scholar
Emanouilidis, E. and Bell, R. A., Latin squares and their inverses, Math. Gaz. 88 (March 2004) pp. 127-128.10.1017/S0025557200174455CrossRefGoogle Scholar
Emanouilidis, E., Powers of Latin squares, Math. Gaz. 90 (November 2006) pp. 478-481.10.1017/S0025557200180398CrossRefGoogle Scholar
Gauthier, N., Integral powers of order three Latin squares, Math. Gaz. 93 (March 2009) pp. 42-49.10.1017/S0025557200184165CrossRefGoogle Scholar
Hawkins, T., The origins of the theory of group characters, Archive for History of Exact Sciences 7 (1971) pp. 142-170.10.1007/BF00411808CrossRefGoogle Scholar
Hawkins, T., New light on Frobenius’ creation of the theory of group characters, Archive for History of Exact Sciences 12 (1974) pp. 217-243.10.1007/BF00357245CrossRefGoogle Scholar
Johnson, F. W., Latin square determinants, Algebraic, extremal and metric combinatorics, LMS Lecture Notes Series 131, Cambridge University Press (1988) pp. 146-154.Google Scholar
Burn, R. P., Non-Desarguesian planes and weak associativity, Math. Gaz. 101 (November 2017) pp. 458-464.10.1017/mag.2017.127CrossRefGoogle Scholar
Hall, M., The theory of groups, Macmillan (1959).Google Scholar
Siu, M.-K., Which Latin squares are Cayley tables? Amer. Math. Monthly 98 (1991) pp. 625-627.10.1080/00029890.1991.11995768CrossRefGoogle Scholar