• Introduction
• Iteration
  • Summation
  • Product
  • Set Notation
  • Nested Iteration
  • Conditions on indices
  • Union and Intersection
  • General Iteration
• General Symbols
  • Cases
  • Function Composition
  • Set Containment
  • Kronecker
• Operations
  • Factorial
  • Binomial
• Differentiation
  • Derivative
  • Partial Derivative
  • Gradient

Gradient $\nabla \operatorname{f}$

The gradient is an extension of the last section. The gradient of a function is a vector containing all its partial derivatives as its components. In the following, we will write all components that the function depends on in a vector $\mathbf{x} = \begin{pmatrix} x_1 \\ \vdots \\ x_n \end{pmatrix}$.

$$\nabla \operatorname{f}(\mathbf{x}) = \begin{pmatrix} \frac{\partial \operatorname{f}(\mathbf{x})}{\partial x_1} \\ \vdots \\ \frac{\partial \operatorname{f}(\mathbf{x})}{\partial x_n} \\ \end{pmatrix}$$

The implementation is basically the same as in the previous section, just with a loop.

Code: