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Classification of conic sections in PE_2(R) (CROSBI ID 205127)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Beban-Brkić, Jelena ; Šimić Horvath, Marija Classification of conic sections in PE_2(R) // Rad Hrvatske akademije znanosti i umjetnosti. Razred za matematičke, fizičke i kemijske znanosti. Matematičke znanosti, 18 (2014), 519; 125-143

Podaci o odgovornosti

Beban-Brkić, Jelena ; Šimić Horvath, Marija

engleski

Classification of conic sections in PE_2(R)

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.

pseudo-Euclidean plane PE_2(R) ; conic section

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Podaci o izdanju

18 (519)

2014.

125-143

objavljeno

1845-4100

Povezanost rada

Matematika