Naslov
Classification of conic sections in PE_2(R)

Autori
Beban-Brkić, Jelena ; Šimić Horvath, Marija

Izvornik
Rad Hrvatske akademije znanosti i umjetnosti. Razred za matematičke, fizičke i kemijske znanosti. Matematičke znanosti (1845-4100) 18 (2014), 519; 125-143

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
pseudo-Euclidean plane PE_2(R) ; conic section

Sažetak
This paper gives a complete classifi cation of conics in PE_2(R). The classifi cation has been made earlier(Reveruk [5]), but it showed to be incomplete and not possible to cite and use in further studies of properties of conics, pencil of conics, and of quadratic forms in pseudo- Euclidean spaces. This paper provides that. A pseudo- orthogonal matrix, pseudo-Euclidean values of a matrix, diagonalization of a matrix in a pseudo-Euclidean way are introduced. Conics are divided in families and by types, giving both of them geometrical meaning. The invariants of a conic with respect to the group of motions in PE_2(R) are determined, making it possible to determine a conic without reducing its equation to canonical form. An overview table is given.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA