Multi Linear Algebra

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,...) %}

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