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I know from earlier that by using Kronecker products we can rewrite matrix multiplication as a matrix multiplying a vector:

$${\bf AB} {\bf \equiv \cases{{\bf M_{AL}} \text{vec}({\bf B}) \\ {\bf M_{BR}} \text{vec}({\bf A})}}$$

$\bf M_{AL}$ is the matrix corresponding to multiplication from left by $\bf A$ and
$\bf M_{BR}$ is the matrix corresponding to multiplication from right by $\bf B$

The $\bf M$ matrices can be systematically constructed using Kronecker products of the ${\bf A}$ (or $\bf B$) matrix and ${\bf I}$.

Matrices are 2-tensors - having 2 indexes (row and column). Can one use kronecker products to create tensor products of higher orders?

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    Have you tried t do it for a $2\times 2 \times 2$ tensor? – 2017-07-06
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    @draks... :I think I did while writing the question, it was like 6 months ago, but maybe i remember the idea if i think for a bit. – 2017-07-06

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