Some results on the structure and spectra of matrix-products
Rutherford, CG (2015). Some results on the structure and spectra of matrix-products. Linear Algebra and Its Applications. 474, pp. 192-212.
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.
|Keywords||trees; caterpillars; P-matrices; matrix spectra|
|Journal||Linear Algebra and Its Applications|
|Journal citation||474, pp. 192-212|
|Digital Object Identifier (DOI)||doi:10.1016/j.laa.2015.02.008|
|06 Mar 2015|
|Publication process dates|
|Deposited||14 Feb 2017|
|Accepted||10 Feb 2015|
|Accepted author manuscript|
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