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Gradient Vector Field
Definition: If f is a scalar function of two variables, then its gradient grad f is defined by grad f(x,y) = f_x(x,y)i + f_y(x,y)j where i and j are the unit vectors <1,0> and <0,1>. Therefore grad f is rally a vector field on R^2 and is called a gradient vector field.
Source: Multivariable Calculus, 7th edition by James Stewart