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

Orthogonal basis

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

$\left\langle v_{i},v_{j}\right\rangle =0{\text{ for }}i\neq j$

holds.