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

Orthonormal 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 orthonormal basis if

$⟨v_i,v_i⟩=1\text{ for all }i\in I\text{ and }⟨v_i,v_j⟩=0\text{ for }i\ne j$

holds.