Thesis (PhD (Mathematical Sciences))--University of Stellenbosch, 2011. / Includes bibliography. / ENGLISH ABSTRACT: Latimer & MacDuffee showed in 1933 that there is a one-to-one correspondence
between equivalence classes of matrices with a given minimum polynomial and
equivalence classes of ideals of a certain ring. In the case where the matrices
are taken over the integers, Behn and Van der Merwe developed an algorithm
in 2002 to produce a representative in each equivalence class. We extend this
algorithm to matrices taken over the ring Fq[T] of polynomials over a finite
field and prove a modified version of the Latimer-MacDuffee theorem which
holds for proper equivalence classes of matrices. / AFRIKAANSE OPSOMMING: Latimer & MacDuffee het in 1933 bewys dat daar 'n een-tot-een korrespondensie
is tussen ekwivalensieklasse van matrikse met 'n gegewe minimumpolinoom
en ekwivalensieklasse van ideale van 'n sekere ring. In die geval waar
die matrikse heeltallige inskrywings het, het Behn en Van der Merwe in 2002
'n algoritme ontwikkel om verteenwoordigers in elke ekwivalensieklas voort te
bring. Ons brei hierdie algoritme uit na die geval van matrikse met inskrywings
in die ring Fq[T] van polinome oor 'n eindige liggaam en ons bewys 'n
gewysigde weergawe van die Latimer-MacDuffee stelling wat geld vir klasse
van streng ekwivalente matrikse.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/6581 |
| Date | 03 1900 |
| Creators | Van Zyl, Jacobus Visser |
| Contributors | Breuer, Florian, University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. |
| Publisher | Stellenbosch : University of Stellenbosch |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 44 p. |
| Rights | University of Stellenbosch |
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