A (d_0 * d_1 * ... * d_{k-1} * d_k) tensor is just a linear map from a (d_0 * d_1 * ... * d_{m-1} * d_{m+1} * ... * d_{k-1} * d_k) tensor to a (d_0 * d_1 * ... * d_{n-1} * d_{n+1} * ... * d_{k-1} * d_k) tensor, where a () tensor is a scalar, right?

(I kid, but I think this is true, right?)