▁and ▁m ▁edges , ▁one ▁can ▁define ▁a ▁matrix ▁with ▁m ▁rows ▁and ▁ nd ▁columns , ▁an ▁expanded ▁version ▁of ▁the ▁inc idence ▁matrix ▁of ▁the ▁graph ▁called ▁the ▁rig id ity ▁matrix . ▁In ▁this ▁matrix , ▁the ▁entry ▁in ▁row ▁e ▁and ▁column ▁( v , i ) ▁is ▁zero ▁if ▁v ▁is ▁not ▁an ▁endpoint ▁of ▁edge ▁e . ▁If , ▁on ▁the ▁other ▁hand , ▁edge ▁e ▁has ▁vertices ▁u ▁and ▁v ▁as ▁end points , ▁then ▁the ▁value ▁of ▁the ▁entry ▁is ▁the ▁difference ▁between ▁the ▁it h ▁coordinates ▁of ▁v ▁and ▁u . ▁ ▁The ▁rig id ity ▁mat roid ▁of ▁the ▁given ▁framework ▁is ▁a ▁linear ▁mat roid ▁that ▁has ▁as ▁its ▁elements ▁the ▁edges ▁of ▁the ▁graph . ▁A ▁set ▁of ▁edges ▁is ▁independent , ▁in ▁the ▁mat roid , ▁if ▁it ▁corresponds ▁to ▁a ▁set ▁of ▁rows ▁of ▁the ▁rig id ity ▁matrix ▁that ▁is ▁linear ly ▁independent . ▁A ▁framework ▁is ▁called ▁generic ▁if ▁the ▁coordinates ▁of ▁its ▁vertices ▁are ▁algebra ically ▁independent ▁real ▁numbers . ▁Any ▁two ▁generic ▁frameworks ▁on ▁the ▁same ▁graph ▁G ▁determine ▁the ▁same ▁rig id ity ▁mat roid , ▁regardless ▁of ▁their ▁specific ▁coordinates . ▁This ▁is ▁the ▁( d - dimensional ) ▁rig id ity ▁mat roid ▁of ▁G . ▁ ▁Stat ics ▁A ▁load ▁on ▁a ▁framework ▁is ▁a ▁system ▁of ▁forces ▁on ▁the ▁vertices ▁( re present ed ▁as ▁vectors ). ▁A ▁stress ▁is ▁a ▁special ▁case ▁of ▁a ▁load , ▁in ▁which ▁equal