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- University
- Politecnico di Milano
- Degree programme
- Computer Engineering
- Subject
- Geometria e Algebra Lineare
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- Notes · Other
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Tabella coniche
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Tabella di riconoscimento delle coniche Data una conica: a x22 b xyc y22 d x2 e y f =0 Si rappresenta mediante le matrici: I 3 = det a b d b c e d e f Invariante cubico I 2 = det a b b c = ac−b2 Invariante quadratico I 1 = Tr a b b c = ac2 Invariante lineare ➢ I3 = 0 (conica degenere) ➢ I2 < 0 → due rette reali distinte ➢ I2 = 0 ➢ Rango(I3) = 2 → coppie di rette reali distinte o complesse coniugate senza punti comuni ➢ Rango(I3) = 1 → coppia di rette reali coincidenti ➢ I2 > 0 → due rette immaginarie coniugate ➢ I3 ≠ 0 (conica non degenere) ➢ I2 < 0 ➢ I1 = 0 → iperbole equilatera ➢ I1 ≠ 0 → iperbole non equilatera ➢ I2 = 0 → parabola ➢ I2 > 0 ➢ I1 ∙ I3 < 0 → ellisse reale ➢ I1 ∙ I3 > 0 → ellisse immaginaria
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