Hints 1: Index notation
edit
Index notation:
-
If
-
-
Dummy indices are replaceable.
Hint 2: Index notation
edit
Hint 3: Index notation
edit
Index notation:
-
From the definition of dyadic product, we can show
-
Contraction gives:
-
Hint 4: Tensor product
edit
Index notation:
-
Definition of dyadics products:
-
We can show that
-
Contraction gives:
-
Hint 5 : Tensor product
edit
Tensor Product of two tensors:
-
Tensor product:
-
Change of basis: Vector transformation rule
-
are the direction cosines.
-
In matrix form
-
Other common form: Vector transformation rule
-
-
In matrix form
-
Change of basis: Tensor transformation rule
-
where are the direction cosines.
In matrix form,
-
Other common form
-
In matrix form,
-