Let and be two second order tensors. Show that
-
Proof:
Using index notation,
-
Hence,
-
Let be a second order tensor and let and be two
vectors. Show that
-
Proof:
It is convenient to use index notation for this. We have
-
Hence,
-
Let be a second order tensors and let and
be two vectors. Show that
-
Proof:
For the first identity, using index notation, we have
-
Hence,
-
For the second identity, we have
-
Therefore,
-
Now, and
. Hence,
-
Therefore,
-