Symmetric bilinear form/Orthogonal basis/Fact

Let ${\displaystyle {}K}$ be a field, and let ${\displaystyle {}V}$ be a finite-dimensional ${\displaystyle {}K}$-vector space endowed with a symmetric bilinear form ${\displaystyle {}\left\langle -,-\right\rangle }$.

Then there exists an

orthogonal basis

on ${\displaystyle {}V}$.