Mathematical Background Linear lnvariant of a rotation matrix Recall: Q=ee+oos p(1-ee)+sin E vect(Q)=vect(sin pE)=sin oe tr(Q)=tr[ee+cos p(1-eeT e e+cos(3 -ee)=1+2cos p tr(Q-1 Define q=sin ge Group into 4-D vector 入≡[,g,g3,o] 三cG l2+⑤≡sin2d+cs32=1 Linear invariant Points on the surface of 4-D |2=q+++=1Mathematical Background • Linear Invariant of a rotation matrix Recall: Define Group into 4-D vector Linear Invariant Points on the surface of 4-D sphere