Example · High school
Terms
| Term | This example | Why |
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| Euclidean norm |
$\norm{x}_2 = \sqrt{3^2 + (-4)^2} = 5$
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The Euclidean norm of $(3, -4)$ is the length of the arrow from the origin, $5$.
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| 1-norm |
$\norm{x}_1 = \abs{3} + \abs{-4} = 7$
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The 1-norm of $(3, -4)$ is $7$, the distance walking $3$ units sideways and then $4$ units down, and its infinity norm, $4$, is the larger of the two moves.
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| infinity norm |
$\norm{x}_{\infty} = \max(\abs{3}, \abs{-4}) = 4$
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