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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| 格式: | text |
| 語言: | English |
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Animo Repository
1999
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| 在線閱讀: | https://animorepository.dlsu.edu.ph/etd_bachelors/16558 |
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| 總結: | 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. |
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