Unit Vector

Last updated Nov 1, 2022

Let $(X, ||\cdot||)$ be a Normed Vector Space. We say $x \in X$ is a Unit Vector if $||x|| = 1$.

1. The Unit Sphere is the Set of Unit Vectors.
2. For any $x \in X$ so that $x \neq 0$, we can rescale it to be a Unit Vector by taking $\hat{x} := \frac{x}{||x||}$.