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.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:uu-488523 |
| Date | January 2022 |
| Creators | Cuszynski-Kruk, Mikolaj |
| Publisher | Uppsala universitet, Algebra, logik och representationsteori |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | U.U.D.M. project report ; 2022:37 |
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