The Euclidean norm $x \mapsto \sqrt{x_1^2 + x_2^2}$ on $\reals^2$

Example · High school

The Euclidean norm, which gives the length of a vector in the plane.

Terms

Term	This example	Why
norm	✓	$x \mapsto \sqrt{x_1^2 + x_2^2}$ is a norm: the Euclidean norm, which comes from the dot product.
covector	✗	The Euclidean norm on $\reals^2$ is not a covector, because it is not linear: the length of $-v$ is the length of $v$, not its negative.

Distinctions using this example

• Norm vs. metric vs. inner product
• Vector vs. covector

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