On matrices having an invariant cone
George Phillip Barker · Czechoslovak Mathematical Journal · 1972
The well known theorems of Perron and Frobenius have been generahzed to operators in a partially ordered Banach space (cf.[7]).This has motivated several authors to consider Hnear operators (or matrices) in a finite dimensional space which leave a cone invariant (cf.[1] and [16]).Our purpose is to continue the exten sions of Perron-Frobenius theory to the more general case of a matrix nonnegative with respect to a cone.We assume a familiarity with the papers of BIRKHOFF [1] and VANDERGRAFT [16].