In a Cartesian coordinate system we have the following relations for a vector field v and a second-order tensor field S . ∇ ∇ ⋅ ⋅ v = ∂ ∂ v i ∂ ∂ x i = v i , i ∇ ∇ ⋅ ⋅ S = ∂ ∂ S i k ∂ ∂ x i e k = S i k , i e k