In determinant as a multilinear map,
given the fact that a multilinear map on (m+n)-tuples of vectors and covectors is a tensor,
What is the "rank" of determinantal multilinear map?
The rank is equivalent to the minimum number of pieces of information needed to represent something in the space.
A determinant is something that has a number of properties and you apply those properties to find the determinant function.
I'm not sure what you mean by the rank of a determinant multi-linear map though.