by using the Brouwer fixed-point theorem
and by studying the dynamics of the action of
on convenient subsets of
.
Full paper in PDF:
$%A. Borobia and U. R. Trías, A geometric proof of the Perron-Frobenius theorem,
Rev. Mat. Univ. Complut. Madrid 5 (1992), no. 1, 57–63.%$
A Geometric Proof of the Perron-Frobenius Theorem
Dpto. Matemáticas UNED 28040 Madrid — Spain | Dpto. Geometría y Topología Universidad Complutense de Madrid 28040 Madrid — Spain |
We obtain an elementary geometrical proof of the classical Perron-Frobenius
theorem for non-negative matrices
by using the Brouwer fixed-point theorem
and by studying the dynamics of the action of
on convenient subsets of
.
1991 Mathematics Subject Classification: 54H20, 15A48.