- be in ▁ ▁as ▁ ▁. ▁ ▁We ▁then ▁have ▁the ▁two ▁orth og on ality ▁relationships ▁ ▁where ▁ ▁is ▁the ▁inverse ▁matrix ▁of ▁the ▁metric ▁ ▁( this ▁comes ▁from ▁subst itut ing ▁the ▁formula ▁for ▁the ▁dual ▁drei - be in ▁in ▁terms ▁of ▁the ▁drei - be in ▁into ▁ ▁and ▁using ▁the ▁orth og on ality ▁of ▁the ▁drei - be ins ). ▁ ▁and ▁ ▁( this ▁comes ▁about ▁from ▁contract ing ▁ ▁with ▁ ▁and ▁using ▁the ▁linear ▁independence ▁of ▁the ▁). ▁It ▁is ▁then ▁easy ▁to ▁verify ▁from ▁the ▁first ▁orth og on ality ▁relation ▁( emp loy ing ▁) ▁that ▁ ▁we ▁have ▁obtained ▁a ▁formula ▁for ▁the ▁inverse ▁metric ▁in ▁terms ▁of ▁the ▁drei - be ins ▁- ▁the ▁drei - be ins ▁may ▁be ▁thought ▁of ▁as ▁the ▁" square - root " ▁of ▁the ▁metric ▁( the ▁physical ▁meaning ▁to ▁this ▁is ▁that ▁the ▁metric ▁, ▁when ▁written ▁in ▁terms ▁of ▁a ▁basis ▁, ▁is ▁locally ▁flat ). ▁Actually ▁what ▁is ▁really ▁considered ▁is ▁ ▁, ▁ ▁which ▁involves ▁the ▁dens it ized ▁drei - be in ▁ ▁instead ▁( dens it ized ▁as ▁). ▁One ▁re co vers ▁from ▁ ▁the ▁metric ▁times ▁a ▁factor ▁given ▁by ▁its ▁determin ant . ▁It ▁is ▁clear ▁that ▁ ▁and ▁ ▁contain ▁the ▁same ▁information , ▁just ▁re arr anged . ▁Now ▁the ▁choice ▁for ▁ ▁is ▁not ▁unique , ▁and ▁in ▁fact ▁one ▁can ▁perform ▁a ▁local ▁in ▁space ▁rotation ▁with