Matrices of the derivative of vectors with respect to vectors (Jacobians) take a specific form:
Here, note that
- each column is the partial of f with respect to one component
, whereas
- each row is the partial of
with respect to the
. That is, the rows ‘cover’ the range of f.
You can then easily remember that C: the columns are components (of the inputs), and R: the rows cover the ranges.