Math Wiki

Gradient as a vector field.

In vector calculus, gradient is the vector (or more specifically, the covector) made from the partial derivatives of a function with respect to each independent variable; as such, it is a special case of the Jacobian matrix. Intuitively, it can thought of as the direction of greatest slope of a graph. It can be calculated by taking the del operator of a scalar function. In three dimensions, it is equal to

In n dimensions, it is equal to

with being the unit vector.

See also