Module_4,Video:Eigenvalues_and_eigenvectors

Course Q&A Math for Machine Learning Linear Algebra for Machine Learning and Data Sc...
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in 0:17 I didn’t understand the instructor when he said take a look at this matrix and how it acts on these points. What does that even mean ? Like, which calculations he used to come up with such result?!

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Matrices apply linear transformation on points. To visualize this, you can see in the plot when you multiply matrix with points, you end up with transformed points . Blue points are original, orange ones are transformed ones.
Figure_1
;
import numpy as np

import matplotlib.pyplot as plt
X,Y=np.meshgrid(np.arange(-1,2),np.arange(-1,2))
points=np.ones((9,2))
points[:,0]=X.ravel()
points[:,1]=Y.ravel()
matr=np.array([[2,1],[0,3]])
new_points=matr@points.T
plt.scatter(X,Y);plt.scatter(new_points.T[:,0],new_points.T[:,1])
<matplotlib.collections.PathCollection object at 0x7f8ba2036860>
<matplotlib.collections.PathCollection object at 0x7f8ba2036b90>
plt.show()

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Great work, thanks!
Could you please suggest a resource to study eigenvalues and eigenvectors

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I dont know any source actually but playing with the last jupyter notebook was really helpful to me.