Graph rigidity for unitarily invariant matrix norms
Metric Geometry
2017-09-27 v1 Combinatorics
Functional Analysis
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.
Keywords
Cite
@article{arxiv.1709.08967,
title = {Graph rigidity for unitarily invariant matrix norms},
author = {Derek Kitson and Rupert H. Levene},
journal= {arXiv preprint arXiv:1709.08967},
year = {2017}
}