Perron–Frobenius theorem and Z≥0[S3]-semimodules

Abstract: In this thesis, the Perron–Frobenius theorem which in its most general formstates that the spectral radius of a non-negative real square matrix is an eigenvaluewith a non-negative eigenvector, is proven. Related properties arederived, in particular the Collatz–Wielandt formula and a general form of anon-negative idempotent matrices. Furthermore, let Rn be the sub-semi-ringof Z≥0[Sn] generated by the Kazhdan–Lusztig basis. a description of R2-semimodules,R3-semi-modules and a classification of elementary R3-semi-modulesis given.