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Nice video!

This was better explained than my course on Mathematical analysis, where the entire course did not provide this high level of explanation and animation. I've been trying to figure out the purpose of these circles, then apply this to linear optimization problems ... thanks to your explanation, I am a step closer to apply these gershgorin circles to sensitivity analysis. Thank you!

Great job but your video needs captions.

Nice. Everything you say of a matrix here can be said of its transpose as well. It'd be an interesting visual, I think, to have two different coloured circles expanding from the 'diagonal points' as epsilon goes from zero to one - one circle expanding as the radius you get from the row of that diagonal entry, one expanding as the radius you get from the column of that diagonal entry.

you should post more videos like this in linear algebra theorems man, very well done and presented, thank you

Just peer reviewed your great work bro, and I also replied you on Bilibili😀

Thanks for sharing this nice Theorem. Some comments on your video: * you are using both j and i to denote the complex unit. Stick to one of them. * many natural questions stay unanswered in the video and should have at least been mentioned: is there one eigenvalue per circle, or can there be a circle with no eigenvalue. Can the eigenvalue be on the boundary? * when you transition eps from 0 to 1 the animation is quite jittery * when a matrix entry is 0, write 0 not 0j (I know, the last two points have to do with Python and Manim, but it is important to learn to use the tool properly, something like this never happened in the videos of 3B1B) * in general, the LaTeX could be improved. Eg set ALL variables in TeX, not in plain text (eg k) * don't be too formal in your written language in videos like this (write "for all" instead of using the symbol; I also recommend this for papers in general) But again, nice video, and I am looking forward to see more! :)

Nice video and animations. Gershgorins theorem was one of my favorite things from my Linear Algebra course. :)

What should I write

Beautyful video, I also like that the proof at the end was not commented and stands for it self. wathched it a couple of times to go by it step by step. watchetime> length video => higher rating of video by the Algo

It's an interesting variation to focus on applications, and leave the proof to the end, instead of the more common other way around. And, of course, we can say more about the eigenvalues than there being k inside a region with k disks: As we increase epsilon, the eigenvalues will never leave "their own" circle.

Still it has more chances of improvement for non mathematical things (like vivid voice or too loud bgm), this topic was so interesting and I can feel the beauty of linear algebras. I haven't thought the complex matrices with such geometric pov. Thank you for the video!

Why did you play 少年たちとの別れ at 9:09 ? I felt like I needed to cry and I didn't know why until I looked up the music. I haven't played Little Busters in six years and apparently it still affects me.

If you/your team animated this, then make your own theme! Y’all are so talented, having your own theme would seriously set you apart from other channels and allow yours to grow

Thanks for sharing this. Another reason to love Linear Algebra.

a caption text would be nice. you're trying for a 'relaxed' voice but for me it became slurred and a bit hard to understand.

The statement of the theorem seems to leave open the possibility that a disc might not have an eigenvalue in it if it intersects with another disc. Does that actually occur or does every disc always have an eigenvalue?

Ay! cool video ever, probably you are next 3b1b

I'm lost. What is that eigenvalue thing?

I heard your love for math

That was really neat! I didn't know this theorem before and you explained it really well

Really really nice video!

Thank you for this video. I have no hope of being a mathematician at my age, but the animations make it possible to build an intuition of what is happening in linear algebra, a beautiful subject.

Some comments to make the proof more rigorous: 1, in "proof of (2)" part, I did not consider the case that matrix have repeated diagonal entries. If that is the case, when epsilon = 0, we will have 2 identical dots. But the theorem still holds true. 2, in "fun fact 2" part, the diagonal entries cannot be zero. For example [1, 0, 0 ,0] meets the criteria, but it's singular. 3, at 12:09, a more rigorous statement is: For all lambda in the spectrum, there exists an eigenvector x such that lambda in the Disk. x is dependent on lambda.