Eigenvalues and Eigenvectors, Imaginary and Real

[EugeneKhutoryansky]

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[upandatom]

Finally. After a 3 year physics degree and never knowing what the heck my professors were talking about when they said "eigenvalue" and "eigenvector", now I understand. And to think it was so simple this entire time. Thanks Eugene, I adore your videos :)

[Ktheweim]

Physics and math become so elegant with the classic music

[WilliamDye-willdye]

I wish there was a way to tell YouTube's ranking algorithms that I truly like a video without having to write a trivial comment. I'd read comments more often if the signal-to-noise ratio was better, yet YouTube's policy encourages us to write a comment even when we don't have anything substantial to contribute. Oh, well. At least the effort is worth it for these videos. I spent many, many hours in math classes dreaming of how mathematics could be better taught by using computer graphics. It's extremely enjoyable to see those old dreams fulfilled by the excellent videos in this channels. I'm deeply grateful to the production team (and a bit jealous). Thanks much!

[zf]

I would love to see a company fully dedicated to publishing content like this. Imagine the impact you could have on the education market. In the same way that Pixar first brought inanimate objects to life, you do the same for mathematics and science. Absolutely amazing.

[EugeneKhutoryansky]

If you like this video, you can help more people find it in their YouTube search engine by clicking the like button, and writing a comment. Thanks.

[vma]

Those of us who are science/engineering students know that we are often told to learn how to handle abstract ideas and concepts. That is indeed a necessary skill, but sometimes a good visualization helps a lot! This video was such a case! Great work!

[Kosumo]

If they had told me eigenvectors could be this interesting I would have payed more attention in linear algebra...

[ammar]

The way of presenting the concept is marvelous. Salute to you. To all of the videos, hats off.

[vector]

Eugene, your videos are THE most informative on the Web. Free of verbiage, well-paced and logical. Now I have at least a starting notion of the eigens. Thank you

[giantneuralnetwork]

Amazing work! I love your visual approach... so much more memorable than just mere words. Was interesting to think the eigenvectors and eigenvalues completely characterize the transformation, hadn't thought of that before.

[alejandrodpg]

Your videos are so helpful; I love Kira's voice too! Thank you so much for the great work you are doing.

[d.munami]

Highly imaginative and visualizing simulation that presents very vivid concept of eigenvalue & eigenvector... Great work

[cerimite]

As a savant, these videos are invaluable my for visualizations of complex patterns, as I understand ideas as "pictures snapshots", mostly, and helps with understanding Solid State Chemistry and Physics. That is so beautiful...

[arongil]

Before I've watched the video:
Yes! I've recently watched 3blue1brown's Essence of Linear Algebra series, which covers eigenvectors and eigenvalues, and I'm excited to see a new perspective on them!

After watching the video:
Great video! I hadn't considered how every vector could be represented in terms of eigenvectors, nor had I really thought about imaginary eigenvectors and eigenvalues.

Thank you for the high quality educational videos!

[stevenschilizzi]

Those animations of yours are always so good for the intuition. Thanks heaps for putting the effort in. I’m sure it will help lots of people get a feel for things. It sure helps me.

[marcobrini]

Eugene, thanks for your work; even watching known concepts in your videos helps for a better understanding and sometimes a useful change in perspective. Your service is highly appreciated.

[DavidSaintloth]

It's funny how these videos within a few minutes make more clear concepts that took me entire weeks to "get" when I was at University.

[hemalatha]

Giving an visual perception for a mathematical concept is the best way to understand. Excellent job. After all these years, now I really know what eigen values are really. Thanks a lot. Keep doing the great job.

[Unboxeverything]

absolutely top class.. couldn't have asked for more.. it is changed the way I see maths.. this video reinforced that math is a tool to study physics.. thank you very much for such a detailed lesson..