Definition:Orthogonal Basis/Bilinear Space

Definition
Let $\mathbb K$ be a field.

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

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

Then $\mathcal B$ is orthogonal $f(b_i, b_j) = 0$ for $i\neq j$.

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

Also see

 * Definition:Symplectic Basis