Since the basis vectors do not vary in a Cartesian coordinate system we have the following relations for the gradients of a scalar field ϕ ϕ , a vector field v, and a second-order tensor field S . ∇ ∇ ϕ ϕ = ∂ ∂ ϕ ϕ ∂ ∂ x i e i = ϕ ϕ , i e i ∇ ∇ v = ∂ ∂ ( v j e j ) ∂ ∂ x i ⊗ ⊗ e i = ∂ ∂ v j ∂ ∂ x i e j ⊗ ⊗ e i = v j , i e j ⊗ ⊗ e i ∇ ∇ S = ∂ ∂ ( S j k e j ⊗ ⊗ e k ) ∂ ∂ x i ⊗ ⊗ e i = ∂ ∂ S j k ∂ ∂ x i e j ⊗ ⊗ e k ⊗ ⊗ e i = S j k , i e j ⊗ ⊗ e k ⊗ ⊗ e i