I am looking into performing a rotation of a 3D vector by a quaternion. I understand this entails pre-multiplying the vector $v$ (made into a "pure" quaternion) with $q$ and then post-multiplying the result by the quaternion conjugate $q*$, hence $p=qvq*.$
However, I am having a hard time understanding how the quaternion product is used to expand this equation in this document I found. Could someone please explain to me how to get the matrix (6) from Equation (5) in this link?
Thanks in advance!