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Multivariate Vector Linear Functions ›

Real Linear Equations ›

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Linear Functions

Definition

A function $f: \R ^n \to \R $ is linear if

$f(x + y) = f(x) + f(y)$ for all $x, y \in \R ^n$ and
$f(\alpha x) = \alpha f(x)$ for all $x \in \R ^n$ and $\alpha \in \R $.

There are simple consequences to these conditions. For example, $f(0) = 0$.