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Linear algebra helps to introduce ellipses and hyberbolas. For example an ellipse can be seen as a transformed circle by a linear application.

There is also this theorem for the curve $ax^2+2bxy+cy^2=1$ : let $t_1$ and $t_2$ denote the eigenvalues of the associated matrix.

  1. If $t_1>0$ and $t_2>0$, then the curve is an ellipse.
  2. If $t_1$ and $t_2$ have opposite signs, then the curve is a hyperbola.

Is there any interesting stuff about parabolae in linear algebra ? Sorry if my question is a bit vague.

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    You should look into [the blue book I describe here.](http://math.stackexchange.com/a/102644/21436) Regards,2012-04-16
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    Thank you ! Does somebody have additionnal comments ?2012-04-16

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