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def power_method(a):
    ## Choose v

    n = len(a)
    x = np.array([1 for i in range(n)])

    v = (1 / np.linalg.norm(x)) * x

    w = a.dot(v)
    lambda_ = np.inner(w, v)
    k = 0

    while np.linalg.norm(w - lambda_ * v) > 0 and k <= 100000:
        v = (1 / np.linalg.norm(w)) * w
        w = a.dot(v)
        lambda_ = np.inner(w, v)
        k += 1