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arXiv · 1709.08967

Graph rigidity for unitarily invariant matrix norms

Derek Kitson·Rupert H. Levene
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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.

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Derek Kitson, Rupert H. Levene. 2017-09-26. Graph rigidity for unitarily invariant matrix norms. https://arxiv.org/abs/1709.08967

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