ABSTRACT
A quadric surface or simply quadric is a surface in 3-space given by an equation of the second degree in the coordinates. It will be convenient to express all vectors in terms of coordinates referred to a right-handed rectangular coordinate system in space. Central quadrics include, for example, spheres, but exclude such quadrics as a cylinder and a paraboloid. The axes of the new coordinate system are called the principal axes of the quadric, and the transformation is often called a transformation to principal axes. It is useful to have a means of recognizing the type of a quadric from its equation without having to reduce it to principal axes. The problem is essentially one of determining the sign of the eigenvalues of a symmetric matrix.
