Some results on the structure and spectra of matrix-products

Journal article

Banaji, M. and Rutherford, C. G. (2015). Some results on the structure and spectra of matrix-products. Linear Algebra and Its Applications. 474, pp. 192-212. https://doi.org/10.1016/j.laa.2015.02.008
AuthorsBanaji, M. and Rutherford, C. G.
Abstract

We consider certain matrix-products where successive matrices in the product belong alternately to a particular qualitative class or its transpose. The main theorems relate structural and spectral properties of these matrix-products to the structure of underlying bipartite graphs. One consequence is a characterisation of caterpillars: a graph is a caterpillar if and only if all matrix-products associated with it have nonnegative real spectrum. Several other equivalences of this kind are proved. The work is inspired by certain questions in dynamical systems where such products arise naturally as Jacobian matrices, and the results have implications for the existence and stability of equilibria in these systems.

Keywordstrees; caterpillars; P-matrices; matrix spectra
Year2015
JournalLinear Algebra and Its Applications
Journal citation474, pp. 192-212
PublisherElsevier
ISSN0024-3795
Digital Object Identifier (DOI)https://doi.org/10.1016/j.laa.2015.02.008
Web address (URL)https://sciencedirect.com/science/article/pii/S0024379515001020?via%3Dihub
Publication dates
Print06 Mar 2015
Publication process dates
Deposited14 Feb 2017
Accepted10 Feb 2015
Accepted author manuscript
Permalink -

https://openresearch.lsbu.ac.uk/item/87701

Download files

Accepted author manuscript
Some_results_on_the_structure_and_spectra_of_matri.pdf
image.gif

  • 148
    total views
  • 127
    total downloads
  • 0
    views this month
  • 0
    downloads this month

Export as

Related outputs

Generalized pentagonal geometries
Forbes, A. and Rutherford, C. G. (2021). Generalized pentagonal geometries. Journal of Combinatorial Designs. https://doi.org/10.1002/jcd.21811
Pancyclicity when each cycle must pass exactly k Hamilton cycle chords.
Chaouche, FA, Rutherford, CG and Whitty, R (2015). Pancyclicity when each cycle must pass exactly k Hamilton cycle chords. Discussiones Mathematicae Graph Theory. 35 (3), pp. 533-539. https://doi.org/10.7151/dmgt.1818
Objective functions with redundant domains
Affif Chaouche, F., Rutherford, C. and Whitty, R. (2012). Objective functions with redundant domains. Journal of Combinatorial Optimization. 26, pp. 372-384. https://doi.org/10.1007/s10878-012-9468-9
P-matrices and signed digraphs
Banaji, M and Rutherford, CG (2010). P-matrices and signed digraphs. Discrete Mathematics. 311 (4), pp. 295-301. https://doi.org/10.1016/j.disc.2010.10.018
Covering radii are not matroid invariants
Britz, T. and Rutherford, C. (2005). Covering radii are not matroid invariants. 296 (1), pp. 117-120. https://doi.org/10.1016/j.disc.2005.03.002