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arXiv · 1306.3817

Classification of Conic Sections in $PE_2(\mathbb{R})$

Jelena Beban-Brkić·Marija Šimić Horvath
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Abstract

This paper gives a complete classification of conics in $PE_2(\mathbb{R})$. 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 $PE_2(\mathbb{R})$ are determined, making it possible to determine a conic without reducing its equation to canonical form. An overview table is given.

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Jelena Beban-Brkić, Marija Šimić Horvath. 2013-06-17. Classification of Conic Sections in $PE_2(\mathbb{R})$. https://arxiv.org/abs/1306.3817

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