Block representations and spectral properties of constant sum matrices

Hill, Sally, Lettington, Matthew C. ORCID: https://orcid.org/0000-0001-9327-143X and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 2018. Block representations and spectral properties of constant sum matrices. Electronic Journal of Linear Algebra 34 , pp. 170-190. 10.13001/1081-3810.3530

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Abstract

An equivalent representation of constant sum matrices in terms of block-structured matrices is given in this paper. This provides an easy way of constructing all constant sum matrices, including those with further symmetry properties. The block representation gives a convenient description of the dihedral equivalence of such matrices. It is also shown how it can be used to study their spectral properties, giving explicit formulae for eigenvalues and eigenvectors in special situations, as well as for quasi-inverses when these exist.

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
Date of First Compliant Deposit:	12 June 2017
Date of Acceptance:	14 March 2018
Last Modified:	05 May 2023 11:38
URI:	https://orca.cardiff.ac.uk/id/eprint/93660

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