Kroneckerjeva kanonična forma : delo diplomskega seminarja

Maček, Valentina (author), Šivic, Klemen (mentor)

Cilj diplomske naloge je najti čim bolj preprost par matrik, ki je danemu paru matrik ekvivalenten. Naš odgovor se skriva v Kroneckerjevi kanonični formi. Naloga najprej vpelje polinomske matrike in predstavi njihove pomembne lastnosti, nato pa z njihovo pomočjo izpelje Kroneckerjevo kanonično formo in jo karakterizira. Sam postopek izračuna Kroneckerjeve kanonične forme je upodobljen tudi na enostavnih primerih.

• Language: Slovenian
• Keywords: matrični šop, Kroneckerjeva kanonična forma, polinomska matrika, minimalni indeksi, invariantni polinomi, elementarni delitelji
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2025
• PID: 20.500.12556/RUL-170351
• UDC: 512
• COBISS.SI-ID: 241699843
• Publication date in RUL: 04.07.2025

Secondary language

• Language: English
• Title: Kronecker canonical form

Abstract

The aim of this thesis is to find the simplest possible pair of matrices that is equivalent to a given pair of matrices. Our answer lies in the Kronecker canonical form. The thesis first introduces polynomial matrices and presents their key features, and then utilizes them to derive and characterise the Kronecker canonical form. The computation of the Kronecker canonical form is also illustrated with simple examples.

• Keywords: matrix pencil, Kronecker canonical form, polynomial matrix, minimal indices, invariant polynomials, elementary divisors