Vector space/K/Inner product/Orthogonal basis/Definition

Orthogonal basis

Let $V$ be a $𝕂$-vector space, endowed with an inner product. A basis $v_i$, $i\in I$, of $V$ is called an orthogonal basis if

$⟨v_i,v_j⟩=0\text{ for }i\ne j$

holds.