Multi Linear Algebra
Overview
Tensor
A k-tensor on a vector space V is a multilinear function from the Cartesian product of k copies of V to the reals.
{% T : V \times V \times ... \times V \rightarrow \mathbb{R} %}
where T is linear in each argument.
- Range is an arbitrary
field, or
vector space
- Domain is a k Cartesian product of k possibly different vector spaces.
Tensor Product
If T is a k-tensor over V and S is an m tensor over V, then the tensor product of
T and S is defined as
{% T \otimes S (v_i,...,v_k, v_{k+1},... v_{k+m}) = T(v_i,...,v_k) \times S(v_{k+1},... v_{k+m}) %}
Tensor
{% T^i_{j,k} %}
Topics
