plot_matrix_n_evectors_w_eig.py

import seaborn as sns; sns.set()

ax = plt.gca()
ax.set_xlabel('Principal component 1')
ax.set_ylabel('Principal component 2')
plt.scatter(X_raw[:, 0], X_raw[:, 1], c='#663399', alpha=0.5)
plt.scatter(X_mean[0], X_mean[1], c='red', s=50)
plt.axis('equal')

for length, vector in zip(w_12, v_12):
    vector[0] = -vector[0]               # Little tweak the sign 
    dir_ = vector * 3  * np.sqrt(length) # Standard Deviation 3
    start = X_mean; end = start + dir_
    arrowprops = dict(arrowstyle='->', linewidth=2, 
                      shrinkA=0, shrinkB=0, color='red', alpha=0.5)
    ax.annotate('', xy=end, xytext=start, arrowprops=arrowprops)