On superalgebras of matrices with symmetry properties

Lettington, Matthew C. ORCID: https://orcid.org/0000-0001-9327-143X, Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 and Hill, Sally 2017. On superalgebras of matrices with symmetry properties. Linear and Multilinear Algebra 66 (8) , pp. 1538-1563. 10.1080/03081087.2017.1363153

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Abstract

It is known that semi-magic square matrices form a 2-graded algebra or superalgebra with the even and odd subspaces under centre-point reflection symmetry as the two components. We show that other symmetries which have been studied for square matrices give rise to similar superalgebra structures, pointing to novel symmetry types in their complementary parts. In particular, this provides a unifying framework for the composite `most perfect square' symmetry and the related class of `reversible squares'; moreover, the semi-magic square algebra is identified as part of a 2-gradation of the general square matrix algebra. We derive explicit representation formulae for matrices of all symmetry types considered, which can be used to construct all such matrices.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Taylor & Francis
ISSN:	0308-1087
Funders:	Engineering and Physical Sciences Research Council
Date of First Compliant Deposit:	12 June 2017
Date of Acceptance:	14 July 2017
Last Modified:	03 May 2023 03:37
URI:	https://orca.cardiff.ac.uk/id/eprint/93659

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