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master's thesis
Moduli nad domenama glavnih ideala
2017. urn:nbn:hr:166:804578
Plenković, Miro
University of Split
Faculty of Science
Department of Mathematics

Cite this document

Plenković, M. (2017). Moduli nad domenama glavnih ideala (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:804578

Plenković, Miro. "Moduli nad domenama glavnih ideala." Master's thesis, University of Split, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:166:804578

Plenković, Miro. "Moduli nad domenama glavnih ideala." Master's thesis, University of Split, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:166:804578

Plenković, M. (2017). 'Moduli nad domenama glavnih ideala', Master's thesis, University of Split, Faculty of Science, accessed 20 April 2024, https://urn.nsk.hr/urn:nbn:hr:166:804578

Plenković M. Moduli nad domenama glavnih ideala [Master's thesis]. Split: University of Split, Faculty of Science; 2017 [cited 2024 April 20] Available at: https://urn.nsk.hr/urn:nbn:hr:166:804578

M. Plenković, "Moduli nad domenama glavnih ideala", Master's thesis, University of Split, Faculty of Science, Split, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:166:804578

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Metadata
TitleModuli nad domenama glavnih ideala
Title (english)Modules over principal ideal domains
AuthorMiro Plenković
MentorGordan Radobolja (mentor)
Committee memberGordan Radobolja (predsjednik povjerenstva)
Committee memberTanja Vojković (član povjerenstva)
Committee memberJelena Pleština (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Mathematics)
Split
Defense date and country2017-07-06, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Moduli nad domenama glavnih ideala mogu se prikazati kao direktna suma konačno mnogo cikličkih modula, i to na dva različita načina, preko invarijantnih faktora ili elementarnih djelitelja. Ako za domenu glavnih ideala uzmemo konkretno prsten polinoma F[x], možemo promatrati posebne blok-dijagonalne matrice, odnosno linearne operacije čije su matrični prikazi blok-dijagonalni; i to na dva načina (kao i gore), preko invarijantnih faktora ili preko elementarnih djelitelja. Koristeći invarijantne faktore dolazimo do racionalne kanonske forme, a koristeći elementarne djelitelje dolazimo do Jordanove kanonske forme. Racionalna kanonska forma je jednaka za sve slične matrice, pa izmedu ostalog može poslužiti za provjeru sličnosti dvije matrice, a iz Jordanove kanonske forme se, između ostalog, odmah može pročitati karakteristični i minimalni polinom matrice.
Abstract (english)
Modules over principal ideal domains can be as a direct sum of a finite num ber of cyclic modules, in two different ways: using invariant factors or ele mentary divisors. If we take specifically the ring of polynomials F[x] as the principal ideal domain, we can observe special block-diagonal matrices, or li near operators whose matrix representations are block-diagonal, in two diffe rent ways (like above), using invariant factors or elementary divisors. Using invariant factors, we obtain rational canonical form, and using elementary divisors, we obtain Jordan canonical form. Rational canonical form iz the same for all similar matrices, so it is useful to check if two matrices are simi lar. Jordan canonical form is useful because the characteristic and minimal polynomials of a matrix can be read immediately from it.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:804578
Study programmeTitle: Mathematics; specializations in: major in pure mathematics, major in computing, major in teaching
Course: major in computing
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to students and staff of home institution
Terms of useLicence In copyright icon
Created on2018-05-18 14:40:41