A quadric surface in three-dimensional Euclidean space is the zero set of a real polynomial of degree two. Its quadratic part can be written with a symmetric matrix , since the antisymmetric matrix part contributes zero to . An orthogonal diagonalization and a translation expose its geometry: examples include an ellipsoid, an elliptic cone, and a hyperboloid. This affine geometric description allows singular surfaces such as a cone's vertex.
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