Using matrices in studying the replication property for magic squares

• Main Authors: Ang, Annaline G., Martinez, Glenda Pauline C.
• Format: text
• Language: English
• Published: Animo Repository 1997
• Subjects: Matrices; Algebras, Linear; Magic squares; Numbers, Complex
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16430
• Institution: De La Salle University

This thesis presents the replication property of magic squares. It deals mainly with matrices and their properties wherein applications of linear algebra and complex analysis are used. In this thesis, a matrix is called a magic square if the sum of its rows and columns are equal. Any array with the replication property is said to be a linear combination of blow-ups of certain magic squares of sizes 1 X 1, 3 X 3, and 12 X 12. The theorems and propositions stated in this thesis are results from the article given by Daniel Shapiro, A Replication Property for Magic Squares . The researchers give expanded proofs of each theorem since it was not explicitly elaborated on in the article. Mathematical definitions not included in the article are also provided with illustrations for better understanding.