Kitson, Derek and Levene, Rupert H. (2020) Graph rigidity for unitarily invariant matrix norms. Journal of Mathematical Analysis and Applications, 491 (2). ISSN 0022-247X
Full text not available from this repository.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.