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Mathematics-Online course: Linear Algebra - Analytic Geometry - Quadrics

Quadric

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Let $ a$ be a quadratic form, $ \beta$ a linear mapping and $ c\in\mathbb{R}$. The set

$\displaystyle Q=\{x\in\mathbb{R}^n : a(x)+2\beta(x)+c=0\} $

is called quadric.

In terms of matrices $ Q$ can be written as

$\displaystyle Q:\quad x^{\operatorname t}A x + 2b^{\operatorname t}x + c =0 $

where $ a(x)= x^{\operatorname t}A x$ and $ \beta(x)=b^{\operatorname t}x$.
(Authors: App/Burkhardt/Höllig)
  automatically generated 4/21/2005