Linear Mapping

A function f is a linear mapping if it satisfies:

• Additivity: $f(x + y) = f(x) + f(y)$
• Homogeneity: $f(\alpha x) = \alpha f(x)$

Used extensively in graphics, optimization, and neural nets.

Here’s some equations to illustrate the concept:

$$f(x + y) = f(x) + f(y)$$

$$f(\alpha x) = \alpha f(x)$$