Graph rigidity for unitarily invariant matrix norms

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 (In Press)

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.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Mathematical Analysis and Applications
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2604
Subjects:
ID Code:
89361
Deposited By:
Deposited On:
20 Dec 2017 13:56
Refereed?:
Yes
Published?:
In Press
Last Modified:
30 Sep 2020 07:22