and this matrix corresponds to the tensor by the prior construction, which is reminiscent of how it corresponds to a linear map (by multiplying on one side only). These tensors themselves generate a vector space by adding them together and multiplying them by scalars in the usual ways that we do for matrices and functions, and the collection of all such tensors so formed is the "tensor product" formula_22 of the two vector spaces themselves. In fact, this space is equivalent to the space of maps represented by every possible matrix of the above size, as can be seen by noting that the simple tensor products formula_23 (here formula_24 is the basis of the other vector space, formula_9) have a "1" in the formula_26-th position and "0"s everywhere else, which allows them to be multiplied by any number and then added up to get a matrix with arbitrary entries.