Replication property for magic squares

Date of Publication

1999

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Abstract/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.

Abstract Format

html

Language

English

Format

Print

Accession Number

TU09226

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Physical Description

89 leaves

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