def find_eigenvector(A, tolerance=0.00001):
guess = [random.random() for _ in A]
while True:
result = matrix_operate(A, guess)
length = magnitude(result)
next_guess = scalar_multiply(1/length, result)
if distance(guess, next_guess) < tolerance:
return next_guess, length # eigenvector, eigenvalue
guess = next_guess
def find_eigenvector(A, tolerance=0.00001):
guess = [random.random() for _ in A]
while True:
result = matrix_operate(A, guess)
length = magnitude(result)
next_guess = scalar_multiply(1 / length, result)
if distance(guess, next_guess) < tolerance:
return next_guess, length # eigenvector, eigenvalue
guess = next_guess
def project(v, w):
"""return the projection of v onto the direction w"""
projection_length = dot(v, w)
return scalar_multiply(projection_length, w)