Quaternion

Definition

\(\breve{q}=w+x\mathbf{i}+y\mathbf{j}+z\mathbf{k}=(w,\vec{v})\), where \(\vec{v}=[x,y,z]^T\)

\(\breve{q}_1\breve{q}_2=(w_1,\vec{v}_1)(w_2,\vec{v}_2)=(w_1w_2-\vec{v}_1\cdot\vec{v}_2, w_1\vec{v}_2+w_2\vec{v}_1+\vec{v}_1\times\vec{v}_2)\)