ABSTRACT
The general Gram-Schmidt orthonormalization procedure takes a set of nonorthogonal linearly independent functions {fk(x), k = 0, 1, …, n} and constructs step by step a set of n orthonormal functions {ϕk(x), k = 0, 1, …, n} with respect to a real weight function w(x) over an interval [a, b]. On the other hand if the set {fk(x), k = 0, 1, …, n} is linearly dependent, then G-S procedure will yield an orthonormal set {ϕk(x)} that is of lesser dimension than the set {fk(x)}.
