▁and ▁opposite ▁forces ▁are ▁applied ▁to ▁the ▁two ▁end points ▁of ▁each ▁edge ▁( which ▁may ▁be ▁imag ined ▁as ▁a ▁spring ) ▁and ▁the ▁forces ▁formed ▁in ▁this ▁way ▁are ▁added ▁at ▁each ▁vertex . ▁Every ▁stress ▁is ▁an ▁equilibrium ▁load , ▁a ▁load ▁that ▁does ▁not ▁imp ose ▁any ▁transl ational ▁force ▁on ▁the ▁whole ▁system ▁( the ▁sum ▁of ▁its ▁force ▁vectors ▁is ▁zero ) ▁nor ▁any ▁rot ational ▁force . ▁A ▁linear ▁dependence ▁among ▁the ▁rows ▁of ▁the ▁rig id ity ▁matrix ▁may ▁be ▁represented ▁as ▁a ▁self - str ess , ▁an ▁assignment ▁of ▁equal ▁and ▁opposite ▁forces ▁to ▁the ▁end points ▁of ▁each ▁edge ▁that ▁is ▁not ▁ident ically ▁zero ▁but ▁that ▁adds ▁to ▁zero ▁at ▁every ▁vertex . ▁Thus , ▁a ▁set ▁of ▁edges ▁forms ▁an ▁independent ▁set ▁in ▁the ▁rig id ity ▁mat roid ▁if ▁and ▁only ▁if ▁it ▁has ▁no ▁self - str ess . ▁ ▁The ▁vector ▁space ▁of ▁all ▁possible ▁loads , ▁on ▁a ▁system ▁of ▁n ▁vertices , ▁has ▁dimension ▁d n , ▁among ▁which ▁the ▁equilibrium ▁loads ▁form ▁a ▁sub space ▁of ▁dimension ▁. ▁An ▁independent ▁set ▁in ▁the ▁rig id ity ▁mat roid ▁has ▁a ▁system ▁of ▁equilibrium ▁loads ▁whose ▁dimension ▁equals ▁the ▁cardinal ity ▁of ▁the ▁set , ▁so ▁the ▁maximum ▁rank ▁that ▁any ▁set ▁in ▁the ▁mat roid ▁can ▁have ▁is ▁. ▁If ▁a ▁set ▁has ▁this ▁rank , ▁it ▁follows ▁that ▁its ▁set ▁of ▁str esses ▁is ▁the ▁same ▁as ▁the ▁space ▁of ▁equilibrium ▁loads .