%0 Journal Article
%T Classification of conic sections in PE_2(R)
%A Beban-Brki£¿
%A Jelena
%A £¿imi£¿ Horvath
%A Marija
%J -
%D 2014
%X Sa£¿etak This paper gives a complete classification of conics in PE_2(R). The classification 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
%K Pseudo-Euclidean plane PE2(R)
%K conic section
%U https://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=188466