Vol. 10 No. 3 (1990)
Jul-Sep / 1990
Published July 1, 1990
How to Cite
Nicol, Robert. 1990. “An Extension of the Perron-Frobenius Theorem”. Brazilian Journal of Political Economy 10 (3):384-96. https://doi.org/10.1590/0101-31571990-0538.
An extension of the Perron-Frobenius theorem
Abstract
Starting from a rather simple theorem by Scheffold a set of sufficient conditions
is found for the system pAp = Bp to have a solution with p > 1 and p > 0, where A and B are
nxn positive matrices. It is shown that such a system would be an extension of the system
pAp = Ip for which the Perron-Frobenius theorem holds.
JEL Classification: B51.
Keywords: Sraffian analysis production system