# Today I Learned

Some of the things I've learned every day since Oct 10, 2016

## 34: Orthonormal Subsets

An orthonormal subset $S$ of an inner product space $V$ is a subspace for which all vectors are mutually orthogonal ($\forall x \neq y \in S, \langle x, y \rangle = 0$) and are unit vectors ($\forall x \in S, ||x|| = 1$).