able to plot sigma area of multivariable normal distribution

multivariable_normal_sigma.py

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as pat
rot = lambda th:np.array([[np.cos(th),-np.sin(th)],[np.sin(th),np.cos(th)]])

mu = np.array([0.,0.]) 
S = np.array([[1,0],[0,6]]) @ rot(np.pi/3)
x = np.random.multivariate_normal(mu, S,10000)
fig = plt.figure(figsize=(10, 10))
ax = fig.add_subplot(111)
ax.scatter(x[:,0],x[:,1],s = 1)

# draw sigma1
U, s, V = np.linalg.svd(S, full_matrices=True)
rot_mat = U@V
pn = 1. if kaiten[0][1] == 0 else abs(kaiten[0][1])/(kaiten[0][1])
rad = np.arccos(kaiten[0][0])*pn

e2 = pat.Ellipse(xy = mu, width = 2*np.sqrt(s[1]), height = 2*np.sqrt(s[0]), alpha = 0.4,fc = None,ec = "red",
angle = np.rad2deg(rad), label = str(int(np.rad2deg(rad))))
ax.add_patch(e2)
ax.legend()

plt.xlim(-10,10)
plt.ylim(-10,10)

like this