gradient

definition

• contain partial derivative of a function wrt each of its input var, arranged in column vector
• $\nabla f(x)={\left[\begin{array}{llc}\frac{\partial f(x)}{\partial x_1}& \cdot \cdot \cdot & \frac{\partial f(x)}{\partial x_n}\end{array}\right]}^{\top }$
• useful for finding the direction and rate of change of a function at a given point
• used in optimization problems, such as finding the minimum or maximum value of a function, by following the opposite or same direction of the gradient, respectively.
• an affine function