Dual quadric

Similarly, the dual concept exists for planes. A dual quadric is the locus of all planes ${\tt\Pi }$ satisfying a homogeneous quadratic equation:

$${\tt\Pi}^\top {\bf Q}^* {\tt\Pi} = 0$$ (B17)

where ${\bf Q}^*$ is a $3 \times 3$ symmetric matrix only defined up to scale and thus also depends on nine independent parameters.