Perron Frobenius Theorems for the Numerical Range of Semi-Monic Matrix Polynomials
| dc.contributor.author | Förster, Karl-Heinz | |
| dc.contributor.author | Kallus, Paul | |
| dc.date.accessioned | 2021-12-17T10:13:47Z | |
| dc.date.available | 2021-12-17T10:13:47Z | |
| dc.date.issued | 2015-03-12 | |
| dc.description.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 $\beta^m =\text{numerical radius } A(\beta)$ | en |
| dc.identifier.issn | 2197-8085 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/15856 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-14629 | |
| dc.language.iso | en | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.ddc | 510 Mathematik | en |
| dc.subject.other | Perron-Frobenius theory | en |
| dc.subject.other | numerical range | en |
| dc.subject.other | matrix polynomials | en |
| dc.title | Perron Frobenius Theorems for the Numerical Range of Semi-Monic Matrix Polynomials | en |
| dc.type | Research Paper | en |
| dc.type.version | submittedVersion | en |
| tub.accessrights.dnb | free | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |
| tub.series.issuenumber | 2015, 03 | en |
| tub.series.name | Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin | en |
| tub.subject.msc2000 | 15A48 Positive matrices and their generalizations; cones of matrices | en |
| tub.subject.msc2000 | 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory | en |
| tub.subject.msc2000 | 15A22 Matrix pencils | en |
| tub.subject.msc2000 | 15B48 Positive matrices and their generalizations; cones of matrices | en |
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