
Accession Number : AD0610441
Title : A NEW PROOF OF THEOREMS OF PERRON AND FROBENIUS ON NONNEGATIVE MATRICES, II.
Descriptive Note : Technical rept. no. 14,
Corporate Author : NORTH CAROLINA UNIV CHAPEL HILL
Personal Author(s) : Brauer,Alfred
Report Date : SEP 1961
Pagination or Media Count : 12
Abstract : In part I (AD110 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 nonnegative 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 nonnegative matrices was postponed. In this paper a new method for the proof in the case of nonnegative matrices is given. The proofs become much simpler and the computation of the greatest root requires a smaller number of steps. (Author)
Descriptors : (*MATRICES(MATHEMATICS), THEOREMS), MATHEMATICAL LOGIC, COMBINATORIAL ANALYSIS, TOPOLOGY, MATHEMATICS, THEORY
Distribution Statement : APPROVED FOR PUBLIC RELEASE