Some results on the structure and spectra of matrix-products

Banaji, Murad and Rutherford, Carrie (2015) Some results on the structure and spectra of matrix-products. Linear Algebra and its Applications, 474 . pp. 192-212. ISSN 0024-3795 (doi:10.1016/j.laa.2015.02.008)

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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 real nonnegative 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.

Item Type: Article
Research Areas: A. > School of Science and Technology > Design Engineering and Mathematics
Item ID: 20577
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Depositing User: Murad Banaji
Date Deposited: 23 Sep 2016 10:05
Last Modified: 01 Jun 2019 04:26

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