Accession Number : AD0610441

Title :   A NEW PROOF OF THEOREMS OF PERRON AND FROBENIUS ON NON-NEGATIVE 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 (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)

Descriptors :   (*MATRICES(MATHEMATICS), THEOREMS), MATHEMATICAL LOGIC, COMBINATORIAL ANALYSIS, TOPOLOGY, MATHEMATICS, THEORY

Distribution Statement : APPROVED FOR PUBLIC RELEASE