Hi Hussein. Thanks for the articles. Went through this one and the SVD one. They both are tremendous.

I just have one doubt. One line that I am not able to understand. In the “The Plot Thickens” section while explaining new axes you have mentioned this line

“To see how, notice that the new x1 axis in the above figure is a line that satisfies the equation: x2=x1 or x1-x2 = 0 (with respect to the old feature axes).”

I am not able to grasp what it means. can you explain it? How are the new axes linear combination of the old one? How x2 and x1 are equal. Please help