Overview
Multi Linear Algebra is an extension of linear algebra. In particular, multi linear algebra deals with linear transformations of multiple inputs, as opposed to linear transformations of a single input.
Multi Linear Transformation
A multi linear transformation is defined as follows. It is a function of multiple inputs from a set of vectors spaces
{% \phi : V_1 \times ... \times V_n \rightarrow W %}
such that the transformation is linear in each input.
{% \phi(...,\lambda v + \mu w, ...) = \lambda \phi(...,v,...) + \mu \phi(...,w,...) %}