Birkhoff's contraction coefficient

doi:10.1016/j.laa.2004.02.039

Linear Algebra and its Applications

Volume 389, 15 September 2004, Pages 227-234

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Abstract

Presented here is a new proof of the theorem of Garrett Birkhoff which states that multiplication by any positive square matrix induces a contraction mapping on positive projective space with respect to the Hilbert projective metric and also evaluates the contraction coefficient.

MSC

15A48

Keywords

Contraction mapping

Hilbert projective pseudometric

Perron–Frobenius theorem

Linear programming