A pair of functions ϕ_i(x) and ϕ_j(x) are orthonormal if they are orthogonal and each normalized so that integral_a^b [ϕ_i(x)]^2 w(x) d x | = | 1 integral_a^b [ϕ_j(x)]^2 w(x) d x | = | 1. These two conditions can be succinctly written as integral_a^b ϕ_i(x) ϕ_j(x) w(x) d x = δ_(i j), where w(x) is a weighting function and δ_(i j) is the Kronecker delta.

complete biorthogonal system | complete orthogonal system | orthogonal polynomials | orthonormal basis | orthonormal vectors