jacobian

If \(f\) is a function from \(R^n \rightarrow R^m\) then the Jacobian is a \(m\times n\) matrix \(J\) where the \((i,j)\) entry is \(\frac{\partial f_i}{\partial x_j}\). That is, each row of the matrix is the gradient of \(f_i\).

If \(m=1\), that is \(f\) is a scalar function, the Jacobian is just the gradient.