Change of Basis : Data Science Basics

A whole new perspective.

[johnathancorgan]

As always, I enjoyed your content; however I have to say I much prefer the whiteboard style. It's easier to refer to earlier presentation material with a glance than to rewind the video.

[houyao]

I like the intuitive explanation of non-invertible. :)

[mynameis]

From this video, it is easy to make a new one for two topics at the same time: discriminator and Kramer's rule. The second part is so beautiful when you visualize it. It is literally obvious: a proportion of a volume (square) of the subparallelogram (parallelepiped) whose sides are parallel to all axes and has a constraint parallel to one of them (to fit the desired vector which we want to represent in a new basis) to a volume of a parallelogram (parallelepiped) which is from our new basis - it implies from the equality of the pieces of space (just draw). It is so beautiful, I don't know why I never saw that anywhere :)

Actually, I hated linear algebra for its formal description where you have to either believe in some statements (for example that if rows are linearly independent then columns too) or spend too much affords to understand the formal proofs. But after I graduated and watched the 3b1b playlist I started to visualize everything, searching invariants and geometrical interpretation of things I had to remember and now this is my favourite subject. I believe it is necessary to start the linear algebra course from the system of linear equations with interpretation about a change of basis, and always keep the geometrical interpretation of every algorithm when it is possible.

Excuse me for my terrible English :)

[Christopher_Tron]

Hey man your videos are great and help a lot. Thank you!

[suryaashishece]

To scale back from new basis to old basis, how does adding 1 * v1 + 1 * v2 trace back to old basis (e1 and e2)? Instead should you be using the formula coef_a = X * coef_b, that you derived?

[Set_Get]

Thanks for another well-explained topic. Please consider going back to whiteboard format. Habib

[KimberlyStoTomas]

how is it the coefs b is 1 and 1? I'm a little confused🥹

[dharmharley]

As always, I enjoyed your content; however, I have to say I much prefer the whiteboard style. It's easier to refer to earlier presentation material with a glance than to rewind the video.