Primjene matrica u ravninskoj geometriji

master's thesis

• Author: Ivana Pleše
• Mentor: Rajna Rajić (mentor)
• Committee member: Rajna Rajić (predsjednik povjerenstva)
• Committee member: Ljiljana Arambašić (član povjerenstva)
• Committee member: Boris Guljaš (član povjerenstva)
• Committee member: Ilja Gogić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-11-26, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Iz veze linearnih transformacija i matrica proizlaze najvažnije primjene linearnih transformacija u rješavanju problema u ravnini. U prva dva poglavlja rada, određujemo matrice specijalnih linearnih transformacija ravnine kao što su centralna i osna simetrija ravnine, rotacija i homotetija te ortogonalna projekcija ravnine. U posljednjem poglavlju opisujemo sve projekcije i zrcaljenja ravnine te njihovu vezu s idempotentnim matricama i matricama involucije. Na kraju rada, opisujemo linearne izometrije ravnine.

Abstract (english)

The most important applications of linear transformations in plane geometry, arise from describing them using matrices. In first two chapters, we determine matrix representations of special linear transformations of the plane, such as central and axial symmetry of the plane, rotation, uniform scaling and orthogonal projection. In the last chapter we describe projections and reflections of the plane and their connection to idempotent and involutory matrices. In the last section we describe linear isometries of the plane.

• Keywords: linearne transformacije; matrice; rješavanje problema u ravnini; linearne izometrije ravnine
• Keywords (english): linear transformations; matrices; solving plane geometry problems; linear isometries of the plane
• Language: croatian
• URN:NBN: urn:nbn:hr:217:881227
• Study programme: Title: Mathematics and Computer Science Education; specializations in: Mathematics and Computer Science Education; Course: Mathematics and Computer Science Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-07-14 11:04:54