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Maximum Norm#

Definition: Maximum Norm

The maximum norm on \(\mathbb{R}^n\) is the function \(||\cdot||_{\infty}: \mathbb{R}^n \to \mathbb{R}\) defined as

\[||\boldsymbol{x}||_{\infty} = \max_{i \in \{1, \dotsc, n\}}|x_i|\]

for all vectors \(\boldsymbol{x} \in \mathbb{R}^n\).