Gram-Schmidt algorithm for finding orthogonal basis U in vector space Φ, given a basis V in vector space Φ

gram-schmidt.py

import numpy as np

def proj(u, v):
    return np.multiply(u, (np.inner(u, v)/np.inner(u, u)))

def orthogonal_basis(*V):
  """Uses the Gram-Schmidt algorithm for finding an orthogonal basis of V"""
  U = [None] * len(V)
  
  for k in range(len(V)):
    U[k] = V[k] - sum(proj(U([j], V[k]) for j in range(k))
  
  return U