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Gradient Vector
A gradient vector describes the direction of steepest ascent for a differentiable function.
Contents
Notation
In terms of partial derivatives, the gradient vector of f(x1, x2, ... xn) is [∂f/∂x1 ∂f/∂x2 ... ∂f/∂xn]. The gradient is notated as ∇f.
At a given point p, as long as the function f is differentiable at p, the gradient vector is:
Note the assumption; it is not negligible. For example, (xy)/(x2 + y2) is partially derivable but is itself not totally derivable at point p = [0 0]. Furthermore, it is not derivable if rotated; the basis must be orthonormal.