Degree Project E in Mathematics

  • Date: –16:15
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 Å64119, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala
  • Lecturer: Mikolaj Cuszynski (Uppsala)
  • Website
  • Organiser: Volodymyr Mazorchuk
  • Contact person: Volodymyr Mazorchuk
  • Seminarium

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



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.