What is an Eigenvector?

Iain Explains Signals, Systems, and Digital Comms

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Explains what an Eigenvector is, and uses a change-of-basis example to provide insights into how many eigenvectors exist for a particular transform, and when they are orthogonal.
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Опубликовано:

11 сен 2024

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Комментарии : 25

@AJ-fo3hp 2 года назад

Thank you very much, I have subscribed to wonderful lecturer. Simple, crystal clear thank you

@iain_explains 2 года назад

Great. I'm glad you like the videos.

@ashwith 2 года назад

My first aha moment for eigenvectors was when someone used Fourier series as an analogy - the sinusoids are like eigenvectors while the Fourier coefficients are the eigen values. Of course in hindsight, this analogy isn't a coincidence. The second aha moment was when I saw "eigen faces" in principal component analysis.

@AJ-fo3hp 2 года назад

Could you please provide details on how fourier Series, is it related to projection each frequency component on basis vector. I am eager learn that analogy

@iain_explains 2 года назад

@@AJ-fo3hp Maybe try this video: "Orthogonal Basis Functions in the Fourier Transform" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-n2kesLcPY7o.html

@iain_explains 2 года назад

Thanks for your comment. Yes, these sort of connections are fundamental (and fascinating).

@xaviergelabert6838 2 года назад

Thanks for sharing Iain! would be great to have a follow-up video showing the use of eigenvectors in digital beamforming (i.e. precoding).

@iain_explains 2 года назад

Thanks for the suggestion. That topic is actually in the following video (at the 5:28 time point), but I might also think about making a specific video on Eigenvector Beamforming, as you suggest: "What is Multi Channel Beamforming?" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-e6scR0C4RAc.html

@user-ox9kn5ub1b 2 года назад

👍👍👍👍thank you

@asinegaasinega 2 года назад

Going along the lines, when you have time, would love to hear your explanations for SVD and QR? would really be great with examples in digital comms. Thank you again!

@iain_explains 2 года назад

Thanks for the suggestion. Actually those topics are getting very close to the top of my "to do" list, so hopefully I'll be able to get to them soon.

@tuongnguyen9391 2 года назад

@@iain_explains if the channel is changing too fast, can the computation of the SVD be fast enough to compensate for this change ?

@Edu888777 2 года назад

Show how , why and where to apply eigenvectors would be nice. I made searchs about it but still hard to find applied examples.

@iain_explains 2 года назад

Yes, I agree. Thanks for the suggestion. I've got it on my "to do" list.

@rd-tk6js 2 года назад

well explained, thanks !

@iain_explains 2 года назад

Glad it was helpful!

@tonyxiao4440 2 года назад

waiting for this topic a long time. Thanks for your video.

@iain_explains 2 года назад

My pleasure.

@arjunsnair4986 2 года назад

Thank you sir

@iain_explains 2 года назад

You're welcome.

@foryou7657 2 года назад

I need your help please

@hariharanramamurthy9946 2 года назад

Sir I have watching your signals and systems videos but can you take a real life example and demonstrate the theory and applications sor

@iain_explains 2 года назад

Thanks for the suggestion. I'll try to do it. In the meantime, one real life example is for multi-channel beamforming. See this video at the 5:28 time point: "What is Multi Channel Beamforming?" @

@asinegaasinega 2 года назад

what a shame that engineering books labor on trying to impress students (esp grad books) about proofs from linear theory when one can actually start FIRST by describing the concept like you did.... I detest books that are written for showmanship (and there are plenty of them- and don't get me started with IEEE papers...ahggghhhhhhhhhh.... but thanks anyway (sorry for my rant. i am sick and tired of it)

@iain_explains 2 года назад

I guess different people learn things in different ways. Personally, I think it is important to start with a visual or graphical explanation, and then look to delve deeper, if interested. I'm so glad you agree, and that you're finding the channel useful.