Quadric

In projective 3-space ${\cal P}^3$ similar concepts exist. These are quadrics. A quadric is the locus of all points ${\tt M}$ satisfying a homogeneous quadratic equation:

$${\tt M}^\top {\bf Q} {\tt M} = 0 \, ,$$ (B16)

where ${\bf Q}$ is a $4 \times 4$ symmetric matrix only defined up to scale. A quadric thus depends on nine independent parameters.