A NEW PROOF OF THEOREMS OF PERRON AND FROBENIUS ON NON-NEGATIVE MATRICES, II.
Abstract
In part I (AD-110 398) of this paper a new proof of the theorems of Perron and Frobenius on positive matrices was given and some of their results were improved. Moreover, a method was obtained to compute the greatest positive root of a positive matrix and a characteristic vector belonging to this root as exactly as needed. The same method can be used directly for non-negative matrices. But the proofs are more difficult than for positive matrices. Therefore the results were first published for positive matrices and the publication for the case of non-negative matrices was postponed. In this paper a new method for the proof in the case of non-negative matrices is given. The proofs become much simpler and the computation of the greatest root requires a smaller number of steps. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1961
- Accession Number
- AD0610441
Entities
People
- Alfred Brauer
Organizations
- University of North Carolina at Chapel Hill