On Generalizations of the Perron-Frobenius Theorem.
Abstract
The Perron-Frobenius Theorem states that a matrix with nonnegative entries has at least one nonnegative eigenvalue of maximal absolute value and a corresponding eigenvector with nonnegative components. We discuss generalizations of this celebrated theorem that locate an eigenvalue of maximal absolute value and the components of a corresponding eigenvector within a certain angle of the complex plane depending on the angle which contains the entries of the matrix. A complete description of the 2 x 2 case as well as partial results for the general case are given.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1982
- Accession Number
- ADA120254
Entities
People
- E. G. Straus
- Moshe Goldberg
Organizations
- University of California, Santa Barbara