Krožnice in hermitske matrike

Mihelič, Zdenka (author), Cencelj, Matija (mentor), Starčič, Tadej (comentor)

Vsako krožnico v kompleksni ravnini predstavimo kot rešitev neke kompleksne enačbe in s tem kot hermitsko matriko dimenzije 2 × 2. Na ta način ne dobimo vseh hermitskih matrik, zato pa razumemo hermitske matrike kot posplošene krožnice, ki vključujejo tudi premice v kompleksni ravnini. To uporabimo za obravnavo inverzije preko krožnice in stereografske projekcije.

• Language: Slovenian
• Keywords: analitična geometrija krožnic
• Work type: Undergraduate thesis
• Typology: 2.11 - Undergraduate Thesis
• Organization: PEF - Faculty of Education
• Year: 2016
• PID: 20.500.12556/RUL-86773
• COBISS.SI-ID: 11274057
• Publication date in RUL: 05.09.2017

Secondary language

• Language: English
• Title: Circles and hermitian matrices

Abstract

Every circle in the complex plane is presented as a solution of a complex equation and thus as a hermitian matrix of dimension 2 × 2. Not every hermitian matrix is obtained in this way, but we take the hermitian matrices as generalized circles, these include also lines in the complex plane. We use this to study inversion in a circle and the stereographic projection.

• Keywords: analytic geometry of circles