Definition:Orthogonal Basis/Bilinear Space

Definition
Let $\mathbb K$ be a field.

Let $\left({V, f}\right)$ be a bilinear space over $\mathbb K$ of finite dimension $n > 0$.

Let $\mathcal B = \left({b_1, \ldots, b_n}\right)$ be an ordered basis of $V$.

Then $\mathcal B$ is orthogonal $f \left({b_i, b_j}\right) = 0$ for $i \ne j$.

That is, the matrix of $f$ relative to $\mathcal B$ is diagonal.

Also see

 * Definition:Symplectic Basis