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Graph rigidity for unitarily invariant matrix norms

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Article number124353
<mark>Journal publication date</mark>15/11/2020
<mark>Journal</mark>Journal of Mathematical Analysis and Applications
Issue number2
Volume491
Number of pages30
Publication StatusPublished
Early online date9/07/20
<mark>Original language</mark>English

Abstract

A rigidity theory is developed for bar-joint frameworks in linear matrix spaces endowed with a unitarily invariant norm. Analogues of Maxwell's counting criteria are obtained and minimally rigid matrix frameworks are shown to belong to the matroidal class of (k,l)-sparse graphs for suitable k and l. A characterisation of infinitesimal rigidity is obtained for product norms and it is shown that K_6 - e (respectively, K_7) is the smallest minimally rigid graph for the class of 2 x 2 symmetric (respectively, hermitian) matrices with the trace norm.