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Modules over principal ideal domains
Miro Plenković (2017)
University of Split
University of Split, Faculty of science
Department of Mathematics
Cite this document...

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

Plenković, Miro. "Moduli nad domenama glavnih ideala." Master's thesis, University of Split, 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, 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, University of Split, Faculty of science, accessed 22 March 2019, https://urn.nsk.hr/urn:nbn:hr:166:804578

Plenković M. Moduli nad domenama glavnih ideala [Master's thesis]. Split: University of Split, University of Split, Faculty of science; 2017 [cited 2019 March 22] Available at: https://urn.nsk.hr/urn:nbn:hr:166:804578

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

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
University 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: Matematika; smjerovi: teorijski, računarski, nastavnički
Study programme type: sveučilišni
Study level: diplomski
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourcetext
File originBorn digital
Access conditionsRestricted access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
Created on2018-05-18 14:40:41