# ## MIT License

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# In[3]:
import numpy as np
import numpy.linalg as la
# Here's an example matrix to use with the normal equations:
# In[4]:
eps = 1e-2 # set to 1e-5, 1e-10
A = np.array([
[1, 1],
[eps, 0],
[0, eps],
])
np.set_printoptions(precision=20)
print(A)
print(A.T @ A)
# * What do you notice about the entries of $A^T A$?
# In[3]:
n = 5
A = np.random.randn(5, 5) * 10**-np.linspace(0, -5, n)
la.cond(A)
# In[4]:
la.cond(np.dot(A.T, A))
# * What do you notice about the condition number?
# * What's a general bound? $\operatorname{cond}(AB)\le \dots$?