Faculty of Architecture, University of Zagreb, 10 000 Zagreb, Croatia
Abstract. This paper gives a complete classification of conics in PE2(R). The classification has been made earlier (Reveruk ), 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 PE2(R) are determined, making it possible to determine a conic without reducing its equation to canonical form. An overview table is given.
2010 Mathematics Subject Classification. 51A05, 51N25.
Key words and phrases. Pseudo-Euclidean plane PE2(R), conic section.