A quick trick for computing eigenvalues

Helo! I'm a Brazilian engineer, graduated in 1996. I'm starting to study Data Mining and I needed to review fundamentals of calculus, differential equations and linear algebra that were not visited by me for a long time. For that, I've been watching your videos on Youtube. They are very valuable. Your approaches make matters very enjoyable for us. Thank you very much.

Excellent, thank you grant! On the topic of linear algebra, I have two questions (both regarding ideas for videos): 1. Are there any plans to make a video on how the geometry of some linear transformation L and the geometry of its transpose (or more generally, adjoint) L* relate to each other? My current intuition is that you take the components of each basis vector and turn them into new basis vectors, but it would be awesome to see a better intuition or see that one in video form. 2. Are there any plans to make a video on singular values and singular vectors? I've found that viewing them in terms of polar decomposition (singular values of A are the eigenvalues of sqrt(A*A), and A = S sqrt(A*A), where S is an isometry) is extraordinarily helpful for geometric intuition - you can just rotate A by S* to get S*A = sqrt(A*A) and find S*A's eigenvalues! I think both of these videos would be excellent for people who want to understand how SVD works, which is core to a lot of ML!

Alex Loftus

By the way I am pretty sure I discovered your work by way of A cappella Science, so this video really makes me happy!

Benjamin Bailey

I think you have the + and - switched on the parabola at 11:19

Benjamin Bailey

Very nice trick! I would like to keep it as it is

Excellent video, as are all of yours! I especially enjoyed Tim's mnemonic jingle, which I'll never forget. I wish I'd learned this formula back when I first learned about eigenvalues and eigenvectors!

David Terr

I'm fine with this video covering one special topic, also because it finds common aspects in eigenvalue computation and quadratic formulas. For some unclear reason reason the explanation of where m comes from in quadratic polynomials had me click repeat several times. Can't tell for sure why. Actually everything is explained clearly. Perhaps the animations were just a tad fast.

Lionel Pöffel

Thanks! Just fixed it.

3blue1brown

Good point, I'll add a little snippet at the end for that.

3blue1brown

That's a good way to frame it, thanks!

3blue1brown

Couldn't agree more. This is a little gem. For viewers who know the videos you reference it's a beautiful little bridge. For those who don't, I'm sure it'll make them want to find out more.

I think is better to keep in separate videos, this one is great already

That jingle will be stuck in my head forever now...

Alex Loftus

Very satisfying. This video is a little gem. I vote for keeping this separate from the discussion about calculating eigenvectors.

Robert Berkowitz

Dammit. I have never used eigenvectors in my life, but I will have this jingle stuck in my head for the next two weeks now !

At about 0:45 the animation gets stuck for a very brief moment

Maybe you might wanna add a note on how the first and second rule came to be - I was quite surprised by them

I haven't watched through the linear algebra series, but if you cover eigenvector computation there, I don't think there's any need to repeat it here... or even in a new video. Seems it would just be "compute the eigenvectors now in the same way as before", though maybe that's just showing my lack of imagination! But if there's a direct application of this trick to finding eigenvectors, I think separate videos are fine. It's easy enough to click on to the next one.

Why are the pi creatures getting smushed at some parts of the video? Cool application of your "Easier quadratic formula" classroom lecture!

Burt Humburg

+1 for separate videos.

Edith Dubiner

I’d suggest the criteria for whether to separate two topics is.. if you were to separate them, would those two video share significant redundant information? I don’t know what you plan on saying about eigenvectors, but if the video stands on it’s own and isn’t redundant with this one, then id separate them. Funny enough, this is something I struggle with. I like to explain too much in one place and I lose people’s attention by the end. 😅

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