The Euclidean norm $x \mapsto \sqrt{x_1^2 + x_2^2}$ on $\reals^2$
The Euclidean norm, which gives the length of a vector in the plane.
Terms
| Term | This example | Why |
|---|---|---|
norm |
✓ | |
| covector | ✗ | It is not linear: the length of $-v$ is the length of $v$, not its negative. |
Distinctions using this example
- Vector vs. covector: The Euclidean norm takes a vector and returns a number, but it is not a covector, because it is not linear: $\lVert -x \rVert = \lVert x \rVert$.