On square roots and norms of matrices with symmetry properties

Brunnock, Rochelle, Lettington, Matthew C. ORCID: https://orcid.org/0000-0001-9327-143X and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 2014. On square roots and norms of matrices with symmetry properties. Linear Algebra and its Applications 459 , pp. 175-207. 10.1016/j.laa.2014.06.054

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Abstract

The present work concerns the algebra of semi-magic square matrices. These can be decomposed into matrices of specific rotational symmetry types, where the square of a matrix of pure type always has a particular type. We examine the converse problem of categorising the square roots of such matrices, observing that roots of either type occur, but only one type is generated by the functional calculus for matrices. Some explicit construction methods are given. Moreover, we take an observation by N.J. Higham as a motivation for determining bounds on the operator p-norms of semi-magic square matrices.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Matrix rings; Matrix norms; Matrix square roots; Magic squares
Publisher:	Elsevier
ISSN:	0024-3795
Date of First Compliant Deposit:	30 March 2016
Date of Acceptance:	29 June 2014
Last Modified:	11 Nov 2024 20:00
URI:	https://orca.cardiff.ac.uk/id/eprint/62017

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