The vector $x = (5, 0) \in \reals^2$
Terms
| Term | This example | Why |
|---|---|---|
| Euclidean norm | $\norm{x}_2 = \sqrt{5^2 + 0^2} = 5$ | |
| 1-norm | $\norm{x}_1 = \abs{5} + \abs{0} = 5$ | |
| infinity norm | $\norm{x}_{\infty} = \max(\abs{5}, \abs{0}) = 5$ |
Distinctions using this example
- Types of norms: All three norms of $(5, 0)$ equal $5$, because the vector lies along an axis: the norms differ only for vectors that point between the axes.