Semi-magic squares and their orthogonal complements

Author:

Mayoral Fernando

Abstract

Not long ago I came across the following quiz in the Sunday supplement of the Spanish newspaper El País: Check that it does not matter how you take any four numbers from the following array; provided that no two of them lie in the same row or column, their sum is always the same.This reminded me of magic squares: square matrices where the sum of the elements in each line (row or column) and diagonal is always the same. Magic squares are a topic in recreational mathematics. Usually one looks for magic squares with elements that are integer, positive and different from each other, e.g. 1,2,…, n2 for a n × n as inAccording to a Chinese legend, matrix A appeared engraved on the carapace of a turtle about 2000 BC. On the other hand, matrix B appears in Albrecht Dürer’s engraving Melencholia (1514) [1].

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. The magic renormalisability of affine Gaudin models;Journal of High Energy Physics;2023-12-01

2. Magic square spectra;Linear Algebra and its Applications;2009-05

3. The Moore?Penrose inverse of a semi-magic square is semi-magic;International Journal of Mathematical Education in Science and Technology;2001-07

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