The fundamental issue is that the derivative of a vector with respect to a vector, i.e. formula_24, is often written in two competing ways. If the numerator y is of size "m" and the denominator x of size "n", then the result can be laid out as either an "m×n" matrix or "n×m" matrix, i.e. the elements of y laid out in columns and the elements of x laid out in rows, or vice versa. This leads to the following possibilities: