> [!definition] > > Let $X$ be a [[Vector Space|vector space]] over $F = \complex|\real$. A **seminorm** is a [[Function|function]] $p: X \to \real^+$ such that > - $p(\lambda x) = \abs{\lambda} p(x)$ for all $x \in X, \lambda \in F$. > - $p(x + y) \le p(x) + p(y)$ for all $x, y \in X$ ([[Triangle Inequality]]).