\begin{definition}[Definition:Orthogonal Basis/Bilinear Space]
Let $\mathbb K$ be a field.
Let $\struct {V, f}$ be a bilinear space over $\mathbb K$ of finite dimension $n > 0$.
Let $\BB = \tuple {b_1, \ldots, b_n}$ be an ordered basis of $V$.
Then $\BB$ is '''orthogonal''' {{iff}}:
:$\map f {b_i, b_j} = 0$
for $i \ne j$.
That is, {{iff}} the matrix of $f$ relative to $\BB$ is diagonal.
\end{definition}