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Is it possible to generate an inverse of an order 3 tensor? If so, how? I have been searching for a couple days, and cannot seem to find anything online to help with this.

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    That is a definition of the inverse of a matrix. What do you mean by the inverse of an order 3 _tensor_?2012-06-20

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Think about how to regard an order 3 tensor as a linear map of spaces of the same dimension?

$V^3 \rightarrow \mathbb R$

$V\rightarrow L(V,V)$

$L(V,V)\rightarrow V$

...

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    @QiaochuYuan I would be grateful if you could give me a reference or helpful link to a proof/further exposition on the statement that "no such map can have an inverse".2015-03-11