Proof:
Using the identity we have
Also, using the definition we have
Therefore,
Using the identity we have
Finally, using the relation , we get
Hence,
Let be a vector field and let be a secondorder 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,
