Eigenvalues and Eigenvectors, Imaginary and Real

[@EugeneKhutoryansky]

To see subtitles in other languages: Click on the gear symbol under the video, then click on "subtitles." Then select the language (You may need to scroll up and down to see all the languages available). --To change subtitle appearance: Scroll to the top of the language selection window and click "options." In the options window you can, for example, choose a different font color and background color, and set the "background opacity" to 100% to help make the subtitles more readable. --To turn the subtitles "on" or "off" altogether: Click the "CC" button under the video. --If you believe that the translation in the subtitles can be improved, please send me an email.

[@gvbrandolini]

Interessante.

[@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 :)

[@EugeneKhutoryansky]

Thanks. I am glad you like my videos. Yes, this is a big problem with the way math, physics, and engineering are presently taught. A lot of time is spent talking about things (Eigenvalues, Eigenvectors, etc.) without ever actually explaining what they are.

[@upandatom]

I agree. I understand that there is only so much time to teach everything in a semester, but I feel with this approach the students know HOW to do math but have no idea WHAT they are actually doing. That's how I felt anyway. Even something as common as basic calculus. We were all taught the chain rule, product rule etc, but if you asked anyone of us what we were actually finding the value to, most of us would have no idea, or would only know the text book phrases like "finding area under the curve?"

[@ACoroa]

I can attest to that. My statistics professor definitely glossed over this stuff.

[@WiseandVegan]

So is this so all around the world or are there some universities that actually teach those things properly? Such as high ranked universities etc. If you have any knowledge on that?

[@PhrontDoor]

In physics, it was horribly covered. But I had a teacher do a wonderful explanation in linear-algebra. So the quality of the material can vary widely.

[@EugeneKhutoryansky]

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

[@EugeneKhutoryansky]

I already have a video on imaginary numbers and functions of complex variables. It is at the following link. kzbin.info/www/bejne/mHq8Z5Sefbuap6M

[@TimNGiaGarcia]

Physics Videos by Eugene Khutoryansky

[@frankeinstein719]

Could you tone down the backgroud music? It's too much! Thanks

[@ethanpet113]

Can you explain quaternions, it's important to uniquely identifying a rotation transformation.

[@Bm23CC]

quaternions is hamilton isn't it. He wrote that on a bridge right beside me.

[@WilliamDye-willdye]

I wish there was a way to tell KZbin'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 KZbin'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!

[@EugeneKhutoryansky]

William, I appreciate the time you take to write your comments, and I am very glad that you enjoy my videos as much as you do. Thanks.

[@drvanon]

I suppose I'll fall to the same fate and write a comment as well.

[@pectenmaximus231]

I believe "liking" videos, or adding them to playlists, is sufficient for influencing the algorithm

[@Skynet_the_AI]

@@pectenmaximus231 i believe you're correct.

[@K2theweim]

Physics and math become so elegant with the classic music

[@guitarttimman]

No wonder we are being mocked. We are skilled in so many areas, and yet all we do is find more creative ways to hurt people. Tesla wanted to provide the world with free electricity, but fat ass Westinghouse stopped him. Then realizing how the evil ones would use his inventions, he decided to destroy the blueprints. People don't even realize where we'd be in this point and time if Tesla would've had his way. Instead, we stay trapped by the curse. I mean. Where is fat ass Westinghouse right now? Probably in Hell. Interestingly enough, the ones who stole this technology just want to keep everyone buried. How stupid is it to brag about something from the grave? Useless.

[@guitarttimman]

Yes, come on. Give me the question mark. I bet you eat meat too.

[@guitarttimman]

Do you think I don't know this stuff?

[@xinfuxia3809]

And the voice is perfect for this purpose. Clear and cold without any distraction.

[@corneliariasdita715]

Yes!!! Hungarian rhapsody no. 2 is suitable for this topic

[@vma011]

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!

[@EugeneKhutoryansky]

Thanks.

[@zf164]

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.

[@Kosumo73]

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

[@giannisniper96]

when people say "when will i use this stuff" to me it just sounds like "i'm too dumb to have a job that requires more than typing on a computer or making burgers"

[@seandafny]

+AlternativeFool STATUS: CAPTURED BY ILLUMINATI So there are others then. I am not alone

[@issacarzate707]

Linear Algebra books can't be read that easy and quickly. It requires a lot of attention to fully understand it. Other way, you may end up doing linear transformations without even knowing what that means.

[@EugeneKhutoryansky]

You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link: kzbin.info_video?ref=share&v=8F0gdO643Tc You will then be able to add translations for all the subtitles. You will also be able to provide a translation for the title of the video. Please remember to hit the submit button for both the title and for the subtitles, as they are submitted separately. Details about adding translations is available at support.google.com/youtube/answer/6054623?hl=en Thanks.

[@nachopuma13]

Spanish translation done 👌 waiting the approval

[@rajavikram247]

I was really astonished by your amazing explanation and I really feel great to see a girl explaining complex concepts in a simple way and colouring your curious minds with great concepts..hope you will become world famous one day and receive prestigious prize one day..❤️❤️❤️

[@cephalopodx7587]

Outside of locating a specific vector in time (making a time stamp of its properties), I don't really understand why these are valuable. What are we doing when we apply Eigen Values or Eigen Vectors? It seems handy but for what purpose? Sorry I have no engineering background.

[@ammar510127]

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

[@EugeneKhutoryansky]

Thanks. I am glad you like the way I present the material.

[@vector8310]

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

[@EugeneKhutoryansky]

Thanks for the compliment about my videos.

[@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.

[@EugeneKhutoryansky]

Thanks for the compliment.

[@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!

[@alejandrodpg]

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

[@EugeneKhutoryansky]

Thanks.

[@d.munami6775]

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

[@EugeneKhutoryansky]

Thanks for the compliment.

[@stevenschilizzi4104]

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.

[@EugeneKhutoryansky]

Thanks. I am glad my animations are helpful.

[@Unboxeverything1]

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..

[@rebekahshtayfman1967]

What you're doing is literally both making my life easier, and what I want to do after I graduate. Thank you, from the bottom of my heart

[@cerimite7674]

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...

[@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.

[@EugeneKhutoryansky]

Thanks.

[@deeps-n5y]

The quality of videos on this channel is just WOW ! Please don't stop making them ! Thank you so much for such wonderful explanations!

[@EugeneKhutoryansky]

Thanks for the compliment. More videos are on their way.

[@jianzhao532]

Magnificent ! This video is the most excellent explain about the eigenvalue and Eigenvector that I ever have seen. Thank you for your excellent work. I will introduce it to my students. Thanks Eugene Khutoryansky.

[@EugeneKhutoryansky]

Thanks for the compliment about my video. I hope your students like it.

[@hemalatha794]

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.

[@EugeneKhutoryansky]

Thanks.

[@RaghavendarMurty]

you explain better than most teachers...the animations help a lot too

[@alexandrugheorghe5610]

superb video Eugene (as always). it goes well with your videos on quantum physics

[@EugeneKhutoryansky]

Thanks.

[@cloudyclo]

Eugene! I did not even realize you made a video on this topic until KZbin recommended me this video a few hours after struggling to find clarification on the internet. My god, there is a lack of visual explanations on the net that explain eigenvectors and eigenvalues geometrically so thank you so much. :') You've once again freed my from my mental anguish. Thank you!

[@EugeneKhutoryansky]

Thanks for the compliment. Glad my video was helpful.

[@tahoon2009]

Can't express how i like your visualization, by far best video on youtube for scientific concepts, It's not Just the smart choice of graphics element, i really like how you pick simple example to mirror the idea in visual form, It's subtle talent :D All my respect and best wished

[@pallabidutta7804]

I just don't know what to say because I'm totally speechless. Describing your videos is just beyond words. Before I know these guys(eigenvectors,eigenvalues) only by solving problems. I don't think about them like this before. And of course the imaginary values of eigen values & vectors... before what I can't even imagine, you introduce it to me. Great work!!! God bless you.

[@EugeneKhutoryansky]

Thanks. I am glad you liked my video.

[@rmanovenkatesh]

Brilliant video. Everything is perfect about it. The content, the accent, the graphics and even the backing music. Love your channel, continue the great work :)

[@EugeneKhutoryansky]

Thanks for the compliment about my video. More videos are on their way.

[@dhruvgoyal7163]

Hi Eugene , your videos are super intuitive and magnificent. keep up the great work..

[@EugeneKhutoryansky]

Thanks for the compliment about my videos.

[@danifart]

Genious! The best youtube channel ever! you are making complex math concepts so easy to understand! I wish I had these videos when I was studying my telecommunications engineering degree

[@EugeneKhutoryansky]

Thanks for that really great compliment.

[@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.

[@TheChrasse]

What a coincidence, I just finished the introduction course to linear algebra a couple weeks ago :) Good video again, Eugene! The part where you visualized imaginary eigenvectors was especially interesting, since I were never able to understand what did they even mean during the course. Thank you!

[@EugeneKhutoryansky]

Glad you liked my video, and my explanation of the imaginary components. Thanks.

[@Krokranski]

very nice! Can you also make a video on Lagrange Multipliers? Sometime in the future.

[@richanayak5109]

My goodness!!!! I did never thought that eigen value, eigen vector is such an interesting topic before watching this video. I really salute the way of presentation, and really really appreciate it. Thank you so much for letting the beautiful concept come out through this, which was otherwise hidden ever since.

[@EugeneKhutoryansky]

Thanks. Glad you liked my video.

[@coder0xff]

Would you do a video on tensors?

[@nanak3363]

YESSSSSS !

[@EugeneKhutoryansky]

Yes, I would like to eventually do a video on tensors.

[@mmoose3673]

I really want to see that as well

[@t3db0t97]

Awesome, please do!!

[@Impedancenetwork]

Me too. I am taking a Vector Analysis course now and we are skipping all the sections on tensors. I was so sad to see that in the syllabus. That is a big reason why I took the course. What a shame. Now I have to study them myself and hopefully get a head start by watching one of these videos. These are great!

[@JayLikesLasers]

I'd love to see more videos on linear algebra

[@drangusgrangus]

Jay Smith Check out the great series by 3Blue1Brown

[@300483rahul]

+David Garrett yes that series is amazing, plz watch Jay ..its a must watch

[@maxwellsequation4887]

3b1b series on linear algebra is just AMAZING

[@presentthejackrussell2041]

I learnt this when I was in high school, it is now so much easier to understand in video format. Thanks, I will teach my son using this video instead.

[@jaredthomas183]

There you go... once again youtube made me go to bed at a ridiculous time... This time though the time wasn't wasted. Way to go Eugene! Already subscribed. Will watch all of your vids for sure. Along with @3Blue1Brown channel yours is the absolute gem on youtube. Both, visualisations and explanations are excellent examples of what education is supposed to be all about. Now, if only you could turn those visualisations into interactive apps to play around with, that would be a total mind blow! No need for school anymore :) Heck, within those 12+ minutes I've already learned and understood here more than 4h+ of my math professor's ramblings! He showed me the numbers, but couldn't gain intuition about eigenvectors/values from numbers alone. This video filled the gap. Thanks a lot for this. Appreciate your work and will consider supporting you on patreon. Cheers!

[@EugeneKhutoryansky]

I am glad to hear that my video was useful, and I hope you enjoy all my other videos too. And I really appreciate your interest in supporting me on Patreon. Thanks!

[@hushhushbee1647]

I get completely lost in thoughts when i watch your videos..thank you♥️

[@josemiguelmalonda1890]

This video makes me happy. I was worried about the meaning of the eigenvalues and the eigenvector. It's a long way to go but these videos make the trip happier

[@nemdenemam9753]

you just made it clear what I didn't get about eigenvalues/vectors all throughout my university studies. Thank you for all your amazing videos

[@EugeneKhutoryansky]

Glad my video has helpful. Thanks.

[@TzGiwrgos15]

Beautiful visualizations. They are very helpful in understanding the ideas behind the various topics. Loving the classical music as well :).

[@sohrab1250]

I got the concept after several years of looking for it. That is amazing!

[@anggairawan8772]

have been wondering this for quite sometime, and then this video appears. Great work!

[@EugeneKhutoryansky]

Thanks.

[@shwetasharma5848]

I had always wondered whether all these mathematical concepts had a physical meaning and you just showed it so beautifully. Thank you

[@EugeneKhutoryansky]

Thanks for the compliment.

[@Yagyaansh]

another awesome video!!

[@EugeneKhutoryansky]

Thanks. I am glad you liked it.

[@sandipankumarrmishra4311]

dude your videos actually explain how classroom 2d stuff is visualized in 3d. It's like visualizing the concepts of physics. Great effort

[@rumpole55]

I’ve been trying to understand the eigen cousins for FOUR decades. This was the mist coherent ever. I’ve been playing go even longer and have about the same level of comprehension.

[@gauravkkumar231]

Thanks so much, your video helped in understanding the basic concepts. Looking forward to see more content from you.

[@SciStone]

have you seen 3Blue1Browns video on Eigenvectors and eigenvalues?

[@sruthis7796]

very helpful videos.... please so more videos like this Sir...I am a physics graduate and I am still unaware of many things...Our present education system is made in such a way that whatever taught can be byhearted and reproduced without any knowledge.. Your videos helped me a lot to know the concepts better.. Please continue adding new videos for us........

[@EugeneKhutoryansky]

More videos are on the way. I am glad that my videos are helpful. Thanks.

[@davidben5159]

My God this is just absolutely genius way of explaining the liner transformations of eigenvalues and eigenvectors thank you so much.

[@EugeneKhutoryansky]

Thanks for the compliments.

[@ProAiming1337]

Amazing video! I finally was able to grasp those concepts! Thank you so much :)

[@EugeneKhutoryansky]

Glad my video was helpful and that you liked it. Thanks.

[@leoberges1705]

I love you. I mean it. Thank you so much, your job is just amazing. Every thing becomes so clear. For mankind, I hope you'll never stop doing videos !

[@EugeneKhutoryansky]

Thanks for the compliment. More videos are on their way.

[@josephchamberlin9534]

Absolutely brilliant, I have struggled for years to understand this and now I know. Thank you.

[@EugeneKhutoryansky]

Thanks, and I am glad to hear that my video was helpful.

[@kumarsanu767]

One of the best channel, i'm just wondering,thanks to you and your teammates to help us to gain knowledge

[@John77Doe]

Yes!! A New Years video!!! 👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻

[@carlosdavidnavarrete3317]

Eugene's posts are the best out there. The notion of eigenvalues is important across the natural and social sciences. At least for those of us who care about math and conceptual coherence.

[@ShivaramakrishnaReddy]

Thank you! This is extremely helpful to understand what they are :) I want to see a video on Lagrangian and Hamiltonian as well!

[@EugeneKhutoryansky]

I will add those topics to my list of topics for future videos. Thanks.

[@pD5V0DdsaoVhq]

Exactly what i needed to know, great video. Thanks

[@EugeneKhutoryansky]

Thanks. Glad to hear that my video was helpful.

[@husainmHack]

I have spent ages learning these concepts in university, but we are never told what it means, we just know how to convert question into answer. Yeah, its cancer. This video just cured my cancer :) Thank you so much! Your videos are adding a lot of meaning to the seemingly meaningless tasks we sit and do everyday.

[@EugeneKhutoryansky]

Thanks. Yes, this is a major problem with the way our education system presently works.

[@mdshett2]

Excellent site. Very clear explanations of difficult concepts.

[@EugeneKhutoryansky]

Thanks.

[@JoshuaSalazarMejia]

Amazing video! The best way of Learning Linear Algebra (and math in general) is to see it in 3D. Thanks for your contribution

[@EugeneKhutoryansky]

Thanks for the compliment.

[@jasonchoi6460]

Best Eigenvalue and Eigenvecgor explanation video there is on youtube.

[@EugeneKhutoryansky]

Thanks for the compliment about my video.

[@password6975]

These videos are absolutely brilliant, they allow amazing levels of depth with great beauty

[@EugeneKhutoryansky]

Thanks for the compliment about my videos.

[@TheFight339]

This is by the far the best explanation for eigenvalues and eigenvectors!

[@EugeneKhutoryansky]

Thanks for the compliment about my explanation.

[@pendalink]

These have recently become relevant to most of my courses, and this helped a lot. Great work as usual! :)

[@EugeneKhutoryansky]

Glad to hear that my video was helpful. Thanks.

[@NikeshWasnik]

Loving your videos! Awesomely visualized and explained. Thanks a lot!

[@EugeneKhutoryansky]

Thanks.

[@Haripriya-fn7fg]

U are awesome ,the music behind and the voice is so pleasent which makes me concentrate more !!!thanks

[@EugeneKhutoryansky]

Thanks.

[@rahullyrids4959]

practical example of how to actually use it along with this would be perfect and thanks for creating such useful videos and making science much easier for us.

[@fizzabatool8803]

Very informative video. Easy to comprehend and with the bonus of a classy music. It's like the unification of science and arts..

[@EugeneKhutoryansky]

Thanks.

[@alfonshomac]

Haven't seen you in a while! not a minute in, I trust this video will be worth the up vote and the random comment.

[@greg55666]

Amazing. I have taken 20 different math classes, including linear algebra. I've heard eigenvalues and vectors talked about a thousand times. I have known the math involved, but never ever has it been explained what they ARE. Six minutes of this video would change any young math/physics/engineering student's life.

[@greg55666]

See what I mean? Just click on the video to the right called "Eigenvalues and Eigenvectors," by MIT OpenCourseWare. What a nightmare. I have heard THAT explanation of them a thousand times, and I know how to use them but I've never had any idea what it was about. Unbelievable. Just LOOK at the first 10 seconds of that video. I'm not complaining about the math - math is math, that's fine. I'm talking about the complete lack of UNDERSTANDING that is imparted to the average student on this topic.

[@EugeneKhutoryansky]

Thanks for the compliment about my video. I think the reason that professors teaching at the universities don't explain the physical meaning behind concepts such as this one is because they typically don't understand it themselves. They just know the equations, because this is the way they themselves were taught, and hence they perpetuate this method of explanation, which is really not an explanation at all.

[@greg55666]

I'm glad you said this, because it was exactly what I thought, but I didn't want to say it. :)

[@mohammadfarhikhteh5238]

Amazing Video, a part that I cannot understand from Dynamic within 2 years,now the part is understandable by video 12 minutes,well done.

[@EugeneKhutoryansky]

Thanks.

[@joseph3543]

Great video as always. Great choice of music, also as always!

[@EugeneKhutoryansky]

Thanks. Glad you liked my video.

[@fredericopires7659]

Very very beautiful!!!

[@EugeneKhutoryansky]

Thanks. I am glad you liked my video.

[@VKgaming7447]

this is the most lucid explanation , impeccable way to visualize .

[@EugeneKhutoryansky]

Thanks for the compliment. I am glad you liked my explanation.

[@benokhattirach310]

This is so brilliant and helpful

[@EugeneKhutoryansky]

Thanks for the compliment. I am glad my video is helpful.

[@umeng2002]

Thanks. Even after a Masters in Mechanical Engineering using lots of Eigenvalues and Eigenvectors, I was still having a hard time grasping exactly what they meant. As pointed out, lots of equations and methods are taught, but very little in the way of basic concepts are taught.

[@ashishahuja1914]

Great video, writing a comment in the hope that more of these start popping into my recommendations.

[@EugeneKhutoryansky]

Thanks for the compliment. You don't have to wait for these to start popping up in your recommendations. You can watch all my videos from the "videos" tab on my KZbin home page. Thanks.

[@lizzhancock2698]

Love the vids! The info is awesome and narration/music is so look soothing

[@chaoszwc]

Omg Eugene! Your videos are just amazing! Thanks a lot!

[@mtitut10]

You guys relief me from a frustration scenario. Thank you. Keep it up.

[@anom3778]

Eugenes vids are intensely sophisticated..

[@EugeneKhutoryansky]

Thanks.

[@yuanxu9101]

Very impressed by the video! I like the pace, 3D perspective, and the perfectly mixed music. It would be nice if you can give some references that match your videos. Thanks for your good work! Yuan

[@EugeneKhutoryansky]

Thanks. I am glad that you like my videos. And thanks for the support on Patreon. I really appreciate that.

[@feynstein1004]

Great video as always, Eugene. Can't wait for more.

[@EugeneKhutoryansky]

Glad you liked it. More videos are on their way.

[@Swiitchs]

What I like about your videos, is that it gives me enough time to reason what is going on.

[@y-0790]

Thanks for the videos, i appreciate sharing Knowledge for free.

[@DeusExMachina0000000]

This is helping me understand System-Dynamics and Control Feed back in my ME class. Thank you.

[@EugeneKhutoryansky]

Glad my video was helpful for your class. I also have a video dealing with the topics for that class at kzbin.info/www/bejne/pmrUo3uahaqYaJo

[@DeusExMachina0000000]

HAHA. I saw that one just before this one. Thank you. I like it.

[@tmo7587]

Excellent Video Explanation Eugene!

[@hasinakhyear644]

That rare gold moment when you finally understand some mathematical stuff! I am glad that you exist.

[@EugeneKhutoryansky]

Thanks.

[@safatkhan6839]

That's a very neat explanation! In fact, it's probably the simplest one I've seen so far.

[@sidharthapatnaik5146]

Amazing..... Extra ordinary..... You did a great job....... And we are so helpfull because of you..... I have never thought it like that... I love u..... ❤︎😍

[@EugeneKhutoryansky]

Thanks.

[@adhavankadhiravan4132]

Thank you so much! I never thought Eigen vectors could be this simple to understand.

[@EugeneKhutoryansky]

Glad you liked my video.

[@Jatin19902]

May I please know, which law/theory states that the the number of eigenvectors, and the no. of dimensions of the body under transformation have to be the same i.e. is it possible to have 2 eigenvectors for a 3 dimensional transformation and vice-versa etc. Anyways, thanks a lot for your work.

[@prakashpaudel2708]

One day you will be the greatest youtuber of science videos and will have billions of subscribers. our best wishes are always with you. keep on publishing your great work.

[@EugeneKhutoryansky]

Thanks for that really great compliment. More videos are on their way.

[@manasuniyal2897]

the video was excellent ............ i really understood what actually Eigenvalues and Eigenvectors are...........

[@spacetek2049]

Absolutely FANTASTIC!! (I would lower the music volume a notch...) Thank you for this so-unique production of free videos!

[@dishapanchal3060]

We are really really satisfied with your work. We really appreciate you and your work! Really great experience when we see it! How could you understand all the topic and theories at a time! amazing!👍

[@EugeneKhutoryansky]

Thanks. I am glad you like my videos.

[@dishapanchal3060]

@@EugeneKhutoryansky sir I have a question. I wondered how can you understand the whole theories at a time! how can you? If i want to be like you how can I?