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Graph rigidity for unitarily invariant matrix norms

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Graph rigidity for unitarily invariant matrix norms. / Kitson, Derek; Levene, Rupert H.
In: Journal of Mathematical Analysis and Applications, Vol. 491, No. 2, 124353, 15.11.2020.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Kitson, D & Levene, RH 2020, 'Graph rigidity for unitarily invariant matrix norms', Journal of Mathematical Analysis and Applications, vol. 491, no. 2, 124353. https://doi.org/10.1016/j.jmaa.2020.124353

APA

Kitson, D., & Levene, R. H. (2020). Graph rigidity for unitarily invariant matrix norms. Journal of Mathematical Analysis and Applications, 491(2), Article 124353. https://doi.org/10.1016/j.jmaa.2020.124353

Vancouver

Kitson D, Levene RH. Graph rigidity for unitarily invariant matrix norms. Journal of Mathematical Analysis and Applications. 2020 Nov 15;491(2):124353. Epub 2020 Jul 9. doi: 10.1016/j.jmaa.2020.124353

Author

Kitson, Derek ; Levene, Rupert H. / Graph rigidity for unitarily invariant matrix norms. In: Journal of Mathematical Analysis and Applications. 2020 ; Vol. 491, No. 2.

Bibtex

@article{db6de8a281f24d8fb8e00d7760a3db2f,
title = "Graph rigidity for unitarily invariant matrix norms",
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. ",
author = "Derek Kitson and Levene, {Rupert H.}",
year = "2020",
month = nov,
day = "15",
doi = "10.1016/j.jmaa.2020.124353",
language = "English",
volume = "491",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "2",

}

RIS

TY - JOUR

T1 - Graph rigidity for unitarily invariant matrix norms

AU - Kitson, Derek

AU - Levene, Rupert H.

PY - 2020/11/15

Y1 - 2020/11/15

N2 - 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.

AB - 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.

U2 - 10.1016/j.jmaa.2020.124353

DO - 10.1016/j.jmaa.2020.124353

M3 - Journal article

VL - 491

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

M1 - 124353

ER -