Index notation:
If
Dummy indices are replaceable.
Index notation:
Multiply by :
Multiplication by leads to replacement of one index.
Index notation:
From the definition of dyadic product, we can show
Contraction gives:
Index notation:
Definition of dyadics products:
We can show that
Contraction gives:
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,