On the sum of left and right circulant matrices

Lettington, Matthew ORCID: https://orcid.org/0000-0001-9327-143X and Schmidt, Karl ORCID: https://orcid.org/0000-0002-0227-3024 2023. On the sum of left and right circulant matrices. Linear Algebra and its Applications 658 , pp. 62-85. 10.1016/j.laa.2022.10.024

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Abstract

We consider square matrices arising as the sum of left and right circulant matrices and derive asymptotics of the sequence of their powers. Particular emphasis is laid on the case where the matrix has consecutive integer entries; we find explicit formulae for the eigenvalues and eigenvectors of the matrix in this case and find its Moore-Penrose pseudoinverse. The calculation involves the discrete Fourier transform of integer vectors arising from sum systems and exhibits a resonance phenomenon.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Elsevier
ISSN:	0024-3795
Date of First Compliant Deposit:	3 November 2022
Date of Acceptance:	28 October 2022
Last Modified:	03 May 2023 02:15
URI:	https://orca.cardiff.ac.uk/id/eprint/153884

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