Definition:Orthogonal Basis/Bilinear Space

Definition
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 :
 * $\map f {b_i, b_j} = 0$

for $i \ne j$.

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

Also see

 * Definition:Symplectic Basis