Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14629
 Main Title: Perron Frobenius Theorems for the Numerical Range of Semi-Monic Matrix Polynomials Author(s): Förster, Karl-HeinzKallus, Paul Type: Research Paper URI: https://depositonce.tu-berlin.de/handle/11303/15856http://dx.doi.org/10.14279/depositonce-14629 License: http://rightsstatements.org/vocab/InC/1.0/ Abstract: We present an extension of the Perron-Frobenius theory to the numerical ranges of semi-monic Perron-Frobenius polynomials, namely matrix polynomials of the form $Q(\lambda) = \lambda^m - (\lambda^lA_l + \cdots + A_0) = \lambda^m - A(\lambda),$ where the coefficients are entrywise nonnegative matrices. Our approach relies on the function $\beta \mapsto \text{numerical radius } A(\beta)$ and the infinite graph $G_m(A_0,\ldots, A_l)$. Our main result describes the cyclic distribution of the elements of the numerical range of $Q(\cdot)$ on the circles with radius $\beta$ satisfying $\beta^m =\text{numerical radius } A(\beta)$ Subject(s): Perron-Frobenius theorynumerical rangematrix polynomials Issue Date: 12-Mar-2015 Date Available: 17-Dec-2021 Language Code: en DDC Class: 510 Mathematik MSC 2000: 15A48 Positive matrices and their generalizations; cones of matrices15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory15A22 Matrix pencils15B48 Positive matrices and their generalizations; cones of matrices Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin Series Number: 2015, 03 ISSN: 2197-8085 TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik Appears in Collections: Technische Universität Berlin » Publications