# Presentation av Examensarbete E i matematik

• Datum: –16.15
• Plats: Ångströmlaboratoriet Å64119, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala
• Föreläsare: Mikolaj Cuszynski (Uppsala)
• Webbsida
• Arrangör: Volodymyr Mazorchuk
• Kontaktperson: Volodymyr Mazorchuk

title: Perron-Frobenius theorem and Z_{>=0}[S_3]-semimodules

abstarct:

Presentation of Master Thesis.

In this thesis, Perron-Frobenius theorem which in its most general form states that the spectral radius of a non-negative real square matrix is an eigenvalue with a non-negative eigenvector, is proven.

Related properties are derived, in particular the Collatz–Wielandt formula and a general form of non-negative idempotent matrices. Furthermore, a classification of \$\mathbb{Z}_{\geq 0}[S_2]\$-semimodules with Kazhdan-Lusztig basis and elementary \$\mathbb{Z}_{\geq 0}[S_3]\$-semimodules with Kazhdan-Lusztig basis, is given.