Sometimes, we need to optimize functions whose input and output are vectors. So, for each component of the output vector, we need to compute the gradient vector. For 
, we will have m gradient vectors. By arranging them in a matrix form, we get n x m matrix of partial derivatives 
, called the Jacobian matrix.
For a real-valued function of a single variable, if we want to measure the curvature of the function curve at a point, then we need to compute how first the derivative will change as we change the input. ...
