Let be a vector field and let be a second-order tensor field. Let and be two arbitrary vectors. Show that
Proof:
Using the identity
we have
From the identity
,
we have
.
Since is constant, , and we have
From the relation
we have
Using the relation , we
get
Therefore, the final form of the first term is
For the second term, from the identity
we get,
.
Since is constant, , and we have
From the definition
, we get
Therefore, the final form of the second term is
Adding the two terms, we get
Therefore,