Graph rigidity for unitarily invariant matrix norms (Pre-published)

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Date

2020-11-15

Author

Kitson, Derek

Levene, Rupert H

Peer Reviewed

Yes

Metadata

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Kitson, D. & Levene, R, H. (2020) 'Graph rigidity for unitarily invariant matrix norms', Journal of Mathematical Analysis and Applications, 491(2):124353, https://doi.org/10.1016/j.jmaa.2020.124353 Get rights and content.

Abstract

A rigidity theory is developed for bar-joint frameworks in linear matrix spaces endowed with a unitarily invariant matrix norm. Analogues of Maxwell's counting criteria are obtained and minimally rigid matrix frameworks are shown to belong to the matroidal class of -sparse graphs for suitable k and l. An edge-colouring technique is developed to characterise infinitesimal rigidity for product norms and then applied to show that the graph of a minimally rigid bar-joint framework in the space of 2 x 2 symmetric (respectively, hermitian) matrices with the trace norm admits an edge-disjoint packing consisting of a (Euclidean) rigid graph and a spanning tree.

Keywords

Infinitesimal rigidity
Matrix norm
Matroid
Laman graph

Language (ISO 639-3)

eng

Publisher

Elsevier

Rights

This is the author’s version of a work that was accepted for publication in Journal of Mathematical Analysis and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Mathematical Analysis and Applications, Kitson, D. & Levene, R, H. (2020) 'Graph rigidity for unitarily invariant matrix norms', Journal of Mathematical Analysis and Applications, 491(2):124353. https://www.sciencedirect.com/science/article/pii/S0022247X20305151