Mathematics-Online lexicon: Simplistic Classification of Quadrics

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	Mathematics-Online lexicon:
	Simplistic Classification of Quadrics

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Starting from the equation of a quadric

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

let

$\begin{displaymath} \tilde{A} = \left( \begin{array}{c\vert c} c & b^{\operatorname t}\\ \hline b & A \end{array}\right)\,. \end{displaymath}$

is called

cone quadric, if $\operatorname{Rg}(\tilde{A})=\operatorname{Rg}(A)$ ,
central quadric, if $\operatorname{Rg}(\tilde{A})=\operatorname{Rg}(A)+1$ ,
parabolic quadric, if $\operatorname{Rg}(\tilde{A})=\operatorname{Rg}(A)+2$ ,

see also:

automatically generated 7/13/2018