Let K {\displaystyle {}K} be a field, V {\displaystyle {}V} a K {\displaystyle {}K} -vector space, and let ⟨ − , − ⟩ {\displaystyle {}\left\langle -,-\right\rangle } denote a symmetric bilinear form on V {\displaystyle {}V} . A basis v i {\displaystyle {}v_{i}} , i ∈ I {\displaystyle {}i\in I} , of V {\displaystyle {}V} is called orthogonal basis, if
holds for all i ≠ j {\displaystyle {}i\neq j} .
be a
field,
a
-vector space,
and let 
denote a
symmetric
bilinear form
on . A
basis
, 
,
of is called orthogonal basis, if
.
