On nonsingular regular magic squares of odd order

Michael Z. Lee; Elizabeth Love; Sivaram K. Narayan; Elizabeth Wascher; Jordan D. Webster

doi:10.1016/j.laa.2012.04.004

On nonsingular regular magic squares of odd order

Michael Z. Lee, Elizabeth Love, Sivaram K. Narayan, Elizabeth Wascher, Jordan D. Webster

Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

Using centroskew matrices, we provide a necessary and sufficient condition for a regular magic square to be nonsingular. Using latin squares and circulant matrices we describe a method of construction of nonsingular regular magic squares of order n where n is an odd prime power.

Original language	English
Pages (from-to)	1346-1355
Number of pages	10
Journal	Linear Algebra and Its Applications
Volume	437
Issue number	6
DOIs	https://doi.org/10.1016/j.laa.2012.04.004
State	Published - Sep 15 2012

Keywords

Centroskew matrices
Circulant matrices
Eigenvalues
Latin squares
Magic squares
Regular magic squares

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10.1016/j.laa.2012.04.004

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title = "On nonsingular regular magic squares of odd order",

abstract = "Using centroskew matrices, we provide a necessary and sufficient condition for a regular magic square to be nonsingular. Using latin squares and circulant matrices we describe a method of construction of nonsingular regular magic squares of order n where n is an odd prime power.",

keywords = "Centroskew matrices, Circulant matrices, Eigenvalues, Latin squares, Magic squares, Regular magic squares",

author = "Lee, {Michael Z.} and Elizabeth Love and Narayan, {Sivaram K.} and Elizabeth Wascher and Webster, {Jordan D.}",

note = "Funding Information: Research supported by NSF-REU Grant 05-52594. Corresponding author. Tel.: +1 989 774 3566.",

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AU - Lee, Michael Z.

AU - Love, Elizabeth

AU - Narayan, Sivaram K.

AU - Wascher, Elizabeth

AU - Webster, Jordan D.

N1 - Funding Information: Research supported by NSF-REU Grant 05-52594. Corresponding author. Tel.: +1 989 774 3566.

PY - 2012/9/15

Y1 - 2012/9/15

N2 - Using centroskew matrices, we provide a necessary and sufficient condition for a regular magic square to be nonsingular. Using latin squares and circulant matrices we describe a method of construction of nonsingular regular magic squares of order n where n is an odd prime power.

AB - Using centroskew matrices, we provide a necessary and sufficient condition for a regular magic square to be nonsingular. Using latin squares and circulant matrices we describe a method of construction of nonsingular regular magic squares of order n where n is an odd prime power.

KW - Centroskew matrices

KW - Circulant matrices

KW - Eigenvalues

KW - Latin squares

KW - Magic squares

KW - Regular magic squares

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DO - 10.1016/j.laa.2012.04.004

M3 - Article

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SP - 1346

EP - 1355

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 6

ER -

On nonsingular regular magic squares of odd order

Abstract

Keywords

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