On Bounded Matrices with Non-Negative Elements
- 1 January 1958
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 10, 587-591
- https://doi.org/10.4153/cjm-1958-059-1
Abstract
It is known (Perron (10); Frobenius (5, 6)) that if A = (a ik ) is a finite matrix with elements aik ⩾ 0, then A has a real, nonnegative eigenvalue μ, satisfying μ =max|λ| where λ is in the spectrum of A, with a corresponding eigenvector x = (x 1, … , xn) for which x i≥ 0. Moreover if a ik > 0, then μ is a simple point of the spectrum with an eigenvector x (unique, except for constant multiples) with components xi ≥0. Much has been written on this and related issues; cf., for example, the recent papers (4, 12) wherein are given several references.Keywords
This publication has 1 reference indexed in Scilit:
- A new proof of theorems of Perron and Frobenius on non-negative matrices: I. Positive matricesDuke Mathematical Journal, 1957