The higher rank numerical range of nonnegative matrices

Abstract

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 $C_L$.

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

References in corpus (1)

• The higher rank numerical range of matrix polynomials