Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some results on the structure and spectra of matrix-products   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.

5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th