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.
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 :)
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.
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?"
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?
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.
I wish there was a way to tell RUclips'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 RUclips'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!
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"
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.
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.
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!
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
You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link: ruclips.net/user/timedtext_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.
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..❤️❤️❤️
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.
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.
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!
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.
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...
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.
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..
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
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!
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!
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
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 :)
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
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.
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.
Eugene! I did not even realize you made a video on this topic until RUclips 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!
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.
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.
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.
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 RUclips home page. Thanks.
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!
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!
with enough videos and a solid curriculum you would be better than 90% of college professors out there. You get right to the bottom of the concepts and truth behind all of the dense terminology and math that scares people away from the sciences. Keep up the great work!
Наука
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.
Interessante.
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 :)
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.
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?"
I can attest to that. My statistics professor definitely glossed over this stuff.
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?
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.
Physics and math become so elegant with the classic music
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.
Yes, come on. Give me the question mark. I bet you eat meat too.
Do you think I don't know this stuff?
And the voice is perfect for this purpose. Clear and cold without any distraction.
Yes!!! Hungarian rhapsody no. 2 is suitable for this topic
I wish there was a way to tell RUclips'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 RUclips'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!
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.
I suppose I'll fall to the same fate and write a comment as well.
I believe "liking" videos, or adding them to playlists, is sufficient for influencing the algorithm
@@pectenmaximus231 i believe you're correct.
If they had told me eigenvectors could be this interesting I would have payed more attention in linear algebra...
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"
+AlternativeFool STATUS: CAPTURED BY ILLUMINATI So there are others then. I am not alone
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.
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.
If you like this video, you can help more people find it in their RUclips search engine by clicking the like button, and writing a comment. Thanks.
I already have a video on imaginary numbers and functions of complex variables. It is at the following link.
ruclips.net/video/bIY6ahHVgqA/видео.html
Physics Videos by Eugene Khutoryansky
Could you tone down the backgroud music? It's too much! Thanks
Can you explain quaternions, it's important to uniquely identifying a rotation transformation.
quaternions is hamilton isn't it. He wrote that on a bridge right beside me.
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!
Thanks.
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
Thanks for the compliment about my videos.
The way of presenting the concept is marvelous. Salute to you. To all of the videos, hats off.
Thanks. I am glad you like the way I present the material.
You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link:
ruclips.net/user/timedtext_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.
Spanish translation done 👌 waiting the approval
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..❤️❤️❤️
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.
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.
Thanks for the compliment.
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!
I'd love to see more videos on linear algebra
Jay Smith Check out the great series by 3Blue1Brown
+David Garrett yes that series is amazing, plz watch Jay ..its a must watch
3b1b series on linear algebra is just AMAZING
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
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.
Thanks.
Highly imaginative and visualizing simulation that presents very vivid concept of eigenvalue & eigenvector... Great work
Thanks for the compliment.
Your videos are so helpful; I love Kira's voice too! Thank you so much for the great work you are doing.
Thanks.
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.
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...
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.
Thanks. I am glad my animations are helpful.
very nice!
Can you also make a video on Lagrange Multipliers? Sometime in the future.
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..
superb video Eugene (as always). it goes well with your videos on quantum physics
Thanks.
The quality of videos on this channel is just WOW ! Please don't stop making them !
Thank you so much for such wonderful explanations!
Thanks for the compliment. More videos are on their way.
Thanks so much, your video helped in understanding the basic concepts.
Looking forward to see more content from you.
I get completely lost in thoughts when i watch your videos..thank you♥️
Beautiful visualizations. They are very helpful in understanding the ideas behind the various topics. Loving the classical music as well :).
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
Loving your videos! Awesomely visualized and explained. Thanks a lot!
Thanks.
One of the best channel, i'm just wondering,thanks to you and your teammates to help us to gain knowledge
I got the concept after several years of looking for it. That is amazing!
Would you do a video on tensors?
YESSSSSS !
Yes, I would like to eventually do a video on tensors.
I really want to see that as well
Awesome, please do!!
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!
you explain better than most teachers...the animations help a lot too
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!
Glad you liked my video, and my explanation of the imaginary components. Thanks.
You guys relief me from a frustration scenario. Thank you. Keep it up.
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
These have recently become relevant to most of my courses, and this helped a lot. Great work as usual! :)
Glad to hear that my video was helpful. Thanks.
have been wondering this for quite sometime, and then this video appears. Great work!
Thanks.
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 :)
Thanks for the compliment about my video. More videos are on their way.
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
Thanks for that really great compliment.
Love the vids! The info is awesome and narration/music is so look soothing
Excellent Video Explanation Eugene!
another awesome video!!
Thanks. I am glad you liked it.
Thank you, Eugene. I truly appreciate and enjoy your work :)
Thanks.
Yes!! A New Years video!!! 👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻
Amazing video! I finally was able to grasp those concepts! Thank you so much :)
Glad my video was helpful and that you liked it. Thanks.
Omg Eugene! Your videos are just amazing! Thanks a lot!
Great video as always, Eugene. Can't wait for more.
Glad you liked it. More videos are on their way.
I love it. Linear algebra always fascinates me. I would love to hear more!
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.
Thanks.
dude your videos actually explain how classroom 2d stuff is visualized in 3d. It's like visualizing the concepts of physics. Great effort
Exactly what i needed to know, great video. Thanks
Thanks. Glad to hear that my video was helpful.
Great video as always. Great choice of music, also as always!
Thanks. Glad you liked my video.
Hi Eugene , your videos are super intuitive and magnificent. keep up the great work..
Thanks for the compliment about my videos.
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.
Thanks for the compliment about my video. I hope your students like it.
Thank you! This is extremely helpful to understand what they are :) I want to see a video on Lagrangian and Hamiltonian as well!
I will add those topics to my list of topics for future videos. Thanks.
What I like about your videos, is that it gives me enough time to reason what is going on.
These videos are absolutely brilliant, they allow amazing levels of depth with great beauty
Thanks for the compliment about my videos.
Eugene! I did not even realize you made a video on this topic until RUclips 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!
Thanks for the compliment. Glad my video was helpful.
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.
Thanks. I am glad you liked my video.
I had always wondered whether all these mathematical concepts had a physical meaning and you just showed it so beautifully. Thank you
Thanks for the compliment.
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.
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 !
Thanks for the compliment. More videos are on their way.
As always, a very beautiful visualization!
Thanks for the compliment.
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.
Thanks. Glad you liked my video.
Beautiful illustrations and explanation.
Thanks for the compliment.
Amazing video! The best way of Learning Linear Algebra (and math in general) is to see it in 3D. Thanks for your contribution
Thanks for the compliment.
Absolutely brilliant, I have struggled for years to understand this and now I know. Thank you.
Thanks, and I am glad to hear that my video was helpful.
Your videos are just simply magnificent!!! Thank you very much!
Thanks for the compliment.
Excellent site. Very clear explanations of difficult concepts.
Thanks.
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.
U are awesome ,the music behind and the voice is so pleasent which makes me concentrate more !!!thanks
Thanks.
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.
This is AMAZING, thank you so much and keep up the great work!
Thanks for the compliment. More videos are on their way.
That's a very neat explanation! In fact, it's probably the simplest one I've seen so far.
Great video, writing a comment in the hope that more of these start popping into my recommendations.
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 RUclips home page. Thanks.
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
Glad my video has helpful. Thanks.
Very well explained as always!
Thanks. I am glad you liked my explanation.
My God this is just absolutely genius way of explaining the liner transformations of eigenvalues and eigenvectors thank you so much.
Thanks for the compliments.
Dear Eugene,
Thank you very much for this great video.
You are welcome, and thanks.
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!
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!
beautifully explained
thanks eugene
Thanks.
Amazing explanation on something i was wondering what it is! So many thanks!!!
Glad you liked my explanation.
This is by the far the best explanation for eigenvalues and eigenvectors!
Thanks for the compliment about my explanation.
Beautifully done!
Thanks. I am glad you liked it.
Clearly explained. Thanks for your good work!
Thanks.
Thank you for explaining the physical meaning of these terms.
Amazing Elucidation of Concept.
your videos are GOLD
This is so brilliant and helpful
Thanks for the compliment. I am glad my video is helpful.
Absolutely FANTASTIC!! (I would lower the music volume a notch...) Thank you for this so-unique production of free videos!
Beautiful work! Keep it up
Thank you!
Thank you so much! I never thought Eigen vectors could be this simple to understand.
Glad you liked my video.
Yet another excellent video. Thanks
Thanks.
Great Work and pedagogy !
Thanks.
Thanks for the videos, i appreciate sharing Knowledge for free.
Best Eigenvalue and Eigenvecgor explanation video there is on youtube.
Thanks for the compliment about my video.
Cada uno de sus vídeos es un tesoro invaluable! Saludos desde Colombia.
I love you and your channel so much. This is true beauty :')
Thanks for the compliment.
with enough videos and a solid curriculum you would be better than 90% of college professors out there. You get right to the bottom of the concepts and truth behind all of the dense terminology and math that scares people away from the sciences. Keep up the great work!