Kvadratne forme i krivulje drugog reda

master's thesis

• Author: Petra Petrinjak
• Mentor: Tomislav Šikić (mentor)
• Committee member: Tomislav Šikić (predsjednik povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Pavle Pandžić (član povjerenstva)
• Committee member: Saša Singer (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-07-16, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U radu je opisano kako nastaju konike kao presjek ravnine i dvostrukog stošca, ali je i definirana svaka od krivulja drugog reda te su popisane sve njihove odgovarajuće jednadžbe. Povezana su dva navedena pristupa te je uvedena kvadratna forma povezana sa simetričnim matricama. Uveden je i kanonski oblik kvadratne forme. Potom je dokazano da je simetrična matrica slična dijagonalnoj, a na kraju rada napisano je kako pomoću svojstvenih vrijednosti možemo klasificirati krivulje drugog reda.

Abstract (english)

This work describes how the conics are formed as a section of plane and a double cone, but each of the curves of the second order is defined and all their corresponding equations are listed. Two approaches related to this and a quadratic form of connection with symmetric matrices introduced. The canonical shape of the square form was also introduced. It is then proved that the symmetric matrix is similar to the diagonal and at the end of the paper it is written that by using eigenvalues we can classify curves of the second order.

• Keywords: konike; krivulje drugog reda; simetrične matrice
• Keywords (english): conics; second order curves; symmetric matrices
• Language: croatian
• URN:NBN: urn:nbn:hr:217:881813
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-02-18 10:19:16