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