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Block representations and spectral properties of constant sum matrices

Hill, Sally, Lettington, Matthew C. and Schmidt, Karl Michael 2018. Block representations and spectral properties of constant sum matrices. Electronic Journal of Linear Algebra 34 , pp. 170-190. 10.13001/1081-3810,1537-9582.3530

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Abstract

Using the decomposition of semimagic squares into the associated an d balanced sym- metry types as a motivation, we introduce an equivalent represent ation in terms of block- structured matrices. This block representation provides a way of constructing such matrices with further symmetries and of studying their algebraic behaviour, significantly advancing and contributing to the understanding of these symmetry proper ties. In addition to studying classical attributes, such as dihedral equivalence and the spectr al properties of these matri- ces, we show that the inherent structure of the block represent ation facilitates the definition of low-rank semimagic square matrices. This is achieved by means of t ensor product blocks. Furthermore, we study the rank and eigenvector decomposition o f these matrices, enabling the construction of a corresponding two-sided eigenvector matr ix in rational terms of their entries. The paper concludes with the derivation of a corresponde nce between the tensor product block representations and quadratic form expressions o f Gaussian type.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: International Linear Algebra Society
ISSN: 1537-9582
Funders: Nuffield Foundation, Engineering and Physical Sciences Research Council
Related URLs:
Date of First Compliant Deposit: 12 June 2017
Date of Acceptance: 14 March 2018
Last Modified: 14 Jan 2019 16:30
URI: http://orca.cf.ac.uk/id/eprint/93660

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