\begin{definition}[Definition:Orthonormal Basis of Vector Space]
Let $V$ be a vector space.
Let $\BB = \tuple {\mathbf e_1, \mathbf e_2, \ldots, \mathbf e_n}$ be a basis of $V$.
Then $\BB$ is an '''orthonormal basis of $V$''' {{iff}}:
:$(1): \quad \tuple {\mathbf e_1, \mathbf e_2, \ldots, \mathbf e_n}$ is an orthogonal basis of $V$
:$(2): \quad \norm {\mathbf e_1} = \norm {\mathbf e_2} = \cdots = \norm {\mathbf e_n} = 1$
\end{definition}