▁be ▁expressed ▁as ▁ ▁Exp licit ▁expressions ▁for ▁the ▁gradient ▁If ▁we ▁consider ▁the ▁expression ▁for ▁the ▁tensor ▁in ▁terms ▁of ▁a ▁cont rav ari ant ▁basis , ▁then ▁ ▁We ▁may ▁also ▁write ▁ ▁Represent ing ▁a ▁physical ▁second - order ▁tensor ▁field ▁The ▁physical ▁components ▁of ▁a ▁second - order ▁tensor ▁field ▁can ▁be ▁obtained ▁by ▁using ▁a ▁normal ized ▁cont rav ari ant ▁basis , ▁i . e ., ▁ ▁where ▁the ▁h atted ▁basis ▁vectors ▁have ▁been ▁normal ized . ▁ ▁This ▁implies ▁that ▁( ag ain ▁no ▁summ ation ) ▁ ▁D iver gence ▁ ▁Vector ▁field ▁The ▁diver gence ▁of ▁a ▁vector ▁field ▁() is ▁defined ▁as ▁ ▁In ▁terms ▁of ▁components ▁with ▁respect ▁to ▁a ▁cur vil ine ar ▁basis ▁ ▁An ▁alternative ▁equation ▁for ▁the ▁diver gence ▁of ▁a ▁vector ▁field ▁is ▁frequently ▁used . ▁ ▁To ▁derive ▁this ▁relation ▁recall ▁that ▁ ▁Now , ▁ ▁Not ing ▁that , ▁due ▁to ▁the ▁symmetry ▁of ▁, ▁ ▁we ▁have ▁ ▁Rec all ▁that ▁if ▁[ g ij ] ▁is ▁the ▁matrix ▁whose ▁components ▁are ▁g ij , ▁then ▁the ▁inverse ▁of ▁the ▁matrix ▁is ▁. ▁ ▁The ▁inverse ▁of ▁the ▁matrix ▁is ▁given ▁by ▁ ▁where ▁A ij ▁are ▁the ▁C of actor ▁matrix ▁of ▁the ▁components ▁g ij . ▁ ▁From ▁matrix ▁algebra ▁we ▁have ▁ ▁Hence , ▁ ▁Pl ug ging ▁this ▁relation ▁into ▁the ▁expression ▁for ▁the ▁diver gence ▁gives ▁ ▁A ▁little ▁manip ulation ▁leads ▁to ▁the ▁more ▁compact ▁form ▁