multidimensionalMatrix F
If $F$ is a multilinear form on $\mathbb{P}^{k_1}\times\mathbb{P}^{k_2}\times\cdots\times\mathbb{P}^{k_n}$, then the shape of the corresponding matrix is $(k_1+1)\times(k_2+1)\times\cdots\times(k_n+1)$. You can use permute to rearrange the dimensions.
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The inverse operation can be obtained using the command "!" as follows:
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The source of this document is in SparseResultants.m2:1309:0.