gradient

#machine_learning #calculus

Definition

The gradient of $f$ is the vector of partial derivatives as

\nabla f(\mathbf{x}) = \begin{bmatrix}\frac{\partial f}{\partial x_1}(\mathbf{x})\\ \vdots \\\frac{\partial f}{\partial x_d} (\mathbf{x})\end{bmatrix}

Notes

it may be noted that the gradient may be defined as a linear functional on $\mathbb{R}^n$ and hence belongs to the dual space of $\mathbb{R}^n$

See also

Hessian matrix

References: