The vector $x = (1, 1) \in \reals^2$

Example · High school

Terms

Term	This example	Why
Euclidean norm	$\norm{x}_2 = \sqrt{1^2 + 1^2} = \sqrt{2}$	The three norms of $(1, 1)$ are as far apart as possible for a vector in $\reals^2$: the 1-norm is $\sqrt{2}$ times the Euclidean norm, which is $\sqrt{2}$ times the infinity norm.
1-norm	$\norm{x}_1 = \abs{1} + \abs{1} = 2$
infinity norm	$\norm{x}_{\infty} = \max(\abs{1}, \abs{1}) = 1$

Distinctions using this example

• Types of norms

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