| Title | Moduli nad domenama glavnih ideala |
| Author | Miro Plenković |
| Mentor(s) | Gordan Radobolja (thesis advisor)
|
| 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. |
| Keywords | ring invariant factor elementary divisor matrix Jordan canonical form rational canonical form |
| Parallel title (English) | Modules over principal ideal domains |
| Committee Members | Gordan Radobolja (committee chairperson)
Tanja Vojković (committee member)
Jelena Pleština (committee member)
|
| Granter | University of Split
University of Split, Faculty of science |
| Lower level organizational units | Department of Mathematics |
| Place | Split |
| State | Croatia |
| Scientific field, discipline, subdiscipline | NATURAL SCIENCES
Mathematics
|
| Study programme type | university |
| Study level | graduate |
| Study programme | Mathematics; specializations in: major in pure mathematics, major in computing, major in teaching |
| Study specialization | major in computing |
| Academic title abbreviation | mag. math. |
| Genre | master's thesis |
| Language | Croatian |
| Defense date | 2017-07-06 |
| Parallel 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. |
| Parallel keywords (Croatian) | prsten invarijantni faktor elementarni djelitelj matrica Jordanova kanonska forma racionalna kanonska forma |
| Resource type | text |
| Access condition | Access restricted to students and staff of home institution |
| Terms of use |  |
| URN:NBN | https://urn.nsk.hr/urn:nbn:hr:166:804578 |
