Editing Quadric (section)

==Formulation==
In coordinates {{nowrap|''x''<sub>1</sub>, ''x''<sub>2</sub>, ..., ''x''<sub>''D''+1</sub>}}, the general quadric is thus defined by the [[algebraic equation]]<ref name="geom">Silvio Levy [http://www.geom.uiuc.edu/docs/reference/CRC-formulas/node61.html Quadrics] in "Geometry Formulas and Facts", excerpted from 30th Edition of ''CRC Standard Mathematical Tables and Formulas'', [[CRC Press]], from [[The Geometry Center]] at [[University of Minnesota]]</ref>
:<math>
\sum_{i,j=1}^{D+1} x_i Q_{ij} x_j + \sum_{i=1}^{D+1} P_i  x_i + R = 0
</math>

which may be compactly written in vector and matrix notation as:

:<math>
x Q x^\mathrm{T} + P x^\mathrm{T} + R = 0\,
</math>

where {{nowrap|1=''x'' = (''x''<sub>1</sub>, ''x''<sub>2</sub>, ..., ''x''<sub>''D''+1</sub>)}} is a row [[vector (geometry)|vector]], ''x''<sup>T</sup> is the [[transpose]] of ''x'' (a column vector), ''Q'' is a {{nowrap|(''D'' + 1)&thinsp;×&thinsp;(''D'' + 1)}} [[matrix (mathematics)|matrix]] and ''P'' is a {{nowrap|(''D'' + 1)}}-dimensional row vector and ''R'' a scalar constant.  The values ''Q'', ''P'' and ''R'' are often taken to be over [[real number]]s or [[complex number]]s, but a quadric may be defined over any [[field (mathematics)|field]].