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?!

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.

;

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()

Great work, thanks!

Could you please suggest a resource to study eigenvalues and eigenvectors

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