# 8.4 Linearity

@inproceedings{84L, title={8.4 Linearity}, author={} }

A function f (x) is a linear function of the independent variable x if, and only if, it satisfies two properties. 1. Additivity (or superposition) f (x 1 + x 2) = f (x 1) + f (x 2) for all x 1 and x 2 in the domain of f (x). 2. Homogeneity f (αx) = αf (x) for all x in the domain of f (x) and all scalars α. Examples of static linear systems 1. f (x) = 2x, x ∈ R (All real numbers) f (x 1 + x 2) = 2(x 1 + x 2) = 2x 1 + 2x 2 f (x 1) + f (x 2) = 2x 1 + 2x 2 So, f (x 1 + x 2) = f (x 1) + f (x 2… CONTINUE READING