\begin{definition}[Definition:Orthonormal Basis]
Let $\mathbb F$ be a field.
Let $V$ be a vector space over $\mathbb F$.
Let $S \subset V$ be a subset of $V$.
Then $S$ is an '''orthonormal basis''' {{iff}}:
:$(1): \quad S$ is a basis.
:$(2): \quad S$ is orthonormal.
Category:Definitions/Linear Algebra
\end{definition}