Symmetric bilinear form/Orthogonal basis/Definition

Let ${\displaystyle {}K}$ be a field, ${\displaystyle {}V}$ a ${\displaystyle {}K}$-vector space, and let ${\displaystyle {}\left\langle -,-\right\rangle }$ denote a symmetric bilinear form on ${\displaystyle {}V}$. A basis ${\displaystyle {}v_{i}}$, ${\displaystyle {}i\in I}$, of ${\displaystyle {}V}$ is called orthogonal basis, if

${\displaystyle {}\left\langle v_{i},v_{j}\right\rangle =0\,}$

holds for all ${\displaystyle {}i\neq j}$.