# Notation for set of unit vectors

Is there a standard notation for the set of unit vectors $\{\vec v\ :\ |\vec v|=1\}$?

• Is this relative to a specific vector space, or any vector space with an appropriate norm? – Brian Tung Jun 29 '16 at 22:18
• Right now I'm writing up something on $\Bbb R^n$, but if there's a notation for other spaces, that'd be good to know as well. – user351090 Jun 29 '16 at 22:21

In $\mathbb R^n$, it is common to use $S^{n-1}$ to denote $\{v \in \mathbb R^n : ||v|| = 1\}$.
• typesetting comment, \|v\| makes the lines closer together. compare $\|v\|$ and $||v||$ – JMoravitz Jun 29 '16 at 22:20