# Minkowski inequality

The Minkowski inequality is

$LaTeX: \|x + y\|_p \le \|x\|_p + \|y\|_p,$

where $LaTeX: \|\cdot \|_p$ denotes the $LaTeX: L_p$ norm and $LaTeX: p \ge 1$. Equality holds if, and only if, $LaTeX: x = \alpha y$ for some scalar, $LaTeX: \alpha.$