where I"m" denotes the "m" × "m" identity matrix, and "J" is the "m" × "m" matrix of partial derivatives, evaluated at ("a", "b"). (In the above, these blocks were denoted by X and Y. As it happens, in this particular application of the theorem, neither matrix depends on "a".) The implicit function theorem now states that we can locally express formula_47 as a function of formula_48 if "J" is invertible. Demanding "J" is invertible is equivalent to det "J" ≠ 0, thus we see that we can go back from the primed to the unprimed coordinates if the determinant of the Jacobian "J" is non-zero. This statement is also known as the inverse function theorem.