. ▁Let ▁RA ▁be ▁the ▁position ▁vector ▁of ▁nucle us ▁A ▁and ▁RA 0 ▁the ▁corresponding ▁equilibrium ▁position . ▁Then ▁ ▁is ▁by ▁definition ▁the ▁Cart esian ▁disp lacement ▁coordinate ▁of ▁nucle us ▁A . ▁Wilson ' s ▁ ▁linear izing ▁of ▁the ▁internal ▁cur vil ine ar ▁coordinates ▁q t ▁express es ▁the ▁coordinate ▁St ▁in ▁terms ▁ ▁of ▁the ▁disp lacement ▁coordinates ▁ ▁where ▁s At ▁is ▁known ▁as ▁a ▁Wilson ▁s - vector . ▁If ▁we ▁put ▁the ▁ ▁into ▁a ▁ ▁( 3 N ▁− ▁ 6 ) ▁× ▁ 3 N ▁matrix ▁B , ▁this ▁equation ▁becomes ▁in ▁matrix ▁language ▁ ▁The ▁actual ▁form ▁of ▁the ▁matrix ▁elements ▁ ▁of ▁B ▁can ▁be ▁fairly ▁complicated . ▁Es pecially ▁for ▁a ▁t ors ion ▁angle , ▁which ▁involves ▁ 4 ▁atoms , ▁ ▁it ▁requires ▁ted ious ▁vector ▁algebra ▁to ▁derive ▁the ▁corresponding ▁values ▁of ▁the ▁. ▁See ▁for ▁ ▁more ▁details ▁on ▁this ▁method , ▁known ▁as ▁the ▁Wilson ▁s - vector ▁method , ▁the ▁book ▁by ▁Wilson ▁et ▁al ., ▁or ▁mole cular ▁v ibration . ▁ ▁Now , ▁ ▁In ▁summ ation ▁language : ▁ ▁Here ▁D ▁is ▁a ▁( 3 N ▁− ▁ 6 ) ▁× ▁ 3 N ▁matrix , ▁which ▁is ▁given ▁by ▁( i ) ▁the ▁linear ization ▁of ▁the ▁internal ▁coordinates ▁q ▁( an ▁algebraic ▁process ) ▁ ▁and ▁( ii ) ▁solution ▁of ▁ ▁Wilson ' s ▁G F ▁equations ▁( a ▁numeric ▁process ). ▁▁ ▁Rel ation ▁to ▁E