This is what index notation is good for, and I encourage everyone to learn it. Jacobians are dx_a/dx_b, two indices, and clearly b belongs to the derivative. Wh

This is what index notation is good for, and I encourage everyone to learn it. Jacobians are dx_a/dx_b, two indices, and clearly b belongs to the derivative. Whether it's rows or columns is an implementation detail of how you're storing these numbers. Index notation also seems natural for programming: an element A[i,j] or a slice Z[3,4,:] are precisely this.