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 if and only if:

$\map f {b_i, b_j} = 0$

for $i \ne j$.

That is, if and only if the matrix of $f$ relative to $\BB$ is diagonal.

Also see

• Definition:Symplectic Basis

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