The higher rank numerical range of nonnegative matrices

Details The higher rank numerical range of nonnegative matrices The higher rank numerical range of nonnegative matrices

2011-04-07

arxiv.org/abs/1104.1328v1

Mathematics

Rings and Algebras

13 pages, 5 figures, 17th International Linear Algebra Society Conference (ILAS), Germany 2011

Scientific paper

In this article the well known "Perron-Frobenius theory" is investigated involving the higher rank numerical range $\Lambda_{k}(A)$ of an irreducible and entrywise nonnegative matrix $A$ and extending the notion of elements of maximum modulus in $\Lambda_{k}(A)$. Further, an application of this theory to the $\Lambda_{k}(L(\lambda))$ of a Perron polynomial $L(\lambda)$ is elaborated via its companion matrix $C_{L}$.

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