Replication property for magic squares

This paper is an exposition of Daniel B. Shapiro's article A Replication Property for Magic Squares , published in Mathematics Magazine, Volume 65, Number 3, June 1992. A matrix A is said to have the Replication Property if its derived matrix A' equals a constant matrix plus a shifted vers...

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Bibliographic Details
Main Authors: Angeles, Antonio S., Ramirez, Almario D., III
Format: text
Language:English
Published: Animo Repository 1999
Online Access:https://animorepository.dlsu.edu.ph/etd_bachelors/16558
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Institution: De La Salle University
Language: English
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Summary:This paper is an exposition of Daniel B. Shapiro's article A Replication Property for Magic Squares , published in Mathematics Magazine, Volume 65, Number 3, June 1992. A matrix A is said to have the Replication Property if its derived matrix A' equals a constant matrix plus a shifted version of A. This study presents a solution in finding m x n matrices that possess the Replication Property by using the concepts of matrices, complex numbers and vector spaces. The paper also shows that any array with the replication property is a linear combination of blow-ups of certain squares of sizes 1 x 1, 3 x 3 and 12 x 12.