Python3 Implementation of Gram Schmidt

gram.py

#!/usr/bin/env python3
'''
This is using the lesson from the following PDF:
    https://www.math.tamu.edu/~yvorobet/MATH304-503/Lect3-07web.pdf
'''

def sub_vect(v1,v2):
    sets = []
    if len(v1) != len(v2):
        return -1
    for i in range(len(v1)):
        sets.append(v1[i] - v2[i])
    return sets

def mult_scalar(v,scalar):
    sets = []
    for i in range(len(v)):
        sets.append(v[i] * scalar)
    return sets

def dot_prod(v1,v2):
    sets = []
    if len(v1) != len(v2):
        return -1
    for i in range(len(v1)):
        sets.append(v1[i] * v2[i])
    return sum(sets)

def gram_schmidt(vectors):
    vector_list = []
    counter = 0
    for vector in vectors:
        for v in vector_list:
            vector = sub_vect(vector,mult_scalar(v,dot_prod(vector,v)/dot_prod(v,v)))
        vector_list.append(vector)
    return vector_list

v1 = [4,1,3,-1]
v2 = [2,1,-3,4]
v3 = [1,0,-2,7]
v4 = [6,2,9,-5]
vectors = [v1, v2, v3, v4]

ortho_basis = gram_schmidt(vectors)
print(f"FLAG: {ortho_basis[3][1]:.5f}")