What is an Eigenvector?

  Рет қаралды 433,831

Leios Labs

Leios Labs

Күн бұрын

Hey guys, this is a quick introductory video to what an eigenvector is and how it relates to eigenvalues. It'll be used a lot later on, so it's good to know!
Outside of that, I'm going to try to be way more consistent with my video uploads. It's been forever since my last one and there are reasons for that, but they are not worth mentioning here.
All of the simulations done on this channel can be seen live on:
/ leioslabs
Or after the fact on:
/ @leioslabslive
Which is my second channel for streams and stuff. I've got a bit of a backlog of videos to make, so hopefully everything goes smoothly from here on out!
I am now way more active on twitter, too, so feel free to follow me there (no pressure):
/ leiosos
Outside of that, the background music is from Josh Woodward (sped up 1.5 times). He's a super cool guy, so go check out his stuff, if you can:
www.joshwoodwa...
I think that's all for now, so have a great day, night, afternoon, morning... whatever time it happens to be your time and I'll see you next time!
NOTE: In the visualization of eigenvectors, I plotted only vectors that passed through the origin on (0,0,0), this does not need to be the case! So long as the points are in the right direction, you will have the right vector and you will see only stretching!
Also, discord:
/ discord

Пікірлер: 684
@lradmclovin9
@lradmclovin9 6 жыл бұрын
You just ended years of confusion in 4 minutes. Thank you
@LeiosLabs
@LeiosLabs 6 жыл бұрын
I'm glad it was helpful! =)
@danpal6737
@danpal6737 3 жыл бұрын
me too , but 2 years later, jobless and unmarried.....
@TheyHurry
@TheyHurry Жыл бұрын
Woah I didn't expect Bernie to be studying linear algebra
@snokful
@snokful Жыл бұрын
@@TheyHurry the pen is not as popular as the sword (sadly). but hopefully in the end, mightier.
@lararomao3786
@lararomao3786 Жыл бұрын
Yes ahaha
@yongyoon2157
@yongyoon2157 7 жыл бұрын
Embarrassingly , I admit that finally I got some meaning in eigenvector and eigenvalue after all those years. Thanks for the insight.
@LeiosLabs
@LeiosLabs 7 жыл бұрын
Don't worry, I think everyone knows that feeling! =)
@rickoshea9282
@rickoshea9282 6 жыл бұрын
That's like finally getting the meaning of multiplying but perhaps now you will be motivated to understand an actual application of eigenvectors and why they are important.
@flashlightbug
@flashlightbug 5 жыл бұрын
I couldn't agree with you more. FINALLY!
@ItsNotAllRainbows_and_Unicorns
@ItsNotAllRainbows_and_Unicorns 4 жыл бұрын
The reason why professors who teach just from the book are doing a disservice to their students. I had a friend who took linear algebra with me and after two semesters still asked me 'what is a vector space. The problem issued when the prof never expanded beyond the book. He couldn't be bothered to bring in new material into the class.
@ginebro1930
@ginebro1930 4 жыл бұрын
It's very common to miss the point on eigenvectors, the main reason is because you need to understand what differential equations are for, how these can help solving them and how linear algebra is in fact divided into 2 parts, one for solving normal equiations Ax=b and one for solving differential equations Ax=λx. All of this makes sense much later so it's a hard topic to bring enthusiasm.
@Louis412e
@Louis412e 8 жыл бұрын
i'm a third year physics major and this was the best explanation i've ever seen, by far. good job!
@LeiosLabs
@LeiosLabs 8 жыл бұрын
Thanks, man! I appreciate it!
@isakhammer6558
@isakhammer6558 5 жыл бұрын
same! Difficult subject though
@jessfairbairn4722
@jessfairbairn4722 6 жыл бұрын
You're the first person to have successfully explained eigenvectors in a way I can visualise, so thank you!
@LeiosLabs
@LeiosLabs 6 жыл бұрын
I'm glad it was useful!
@wrcz
@wrcz 4 жыл бұрын
I literally got chills over my spine from finally understanding. And it is so bloody simple! Thank you! Absolutely brilliant
@priyankaverma9668
@priyankaverma9668 7 жыл бұрын
Wonderful explanation. The geometrical meaning of eigen vector is explained very well. ThankYou for such a nice explaination
@LarryPanozzo
@LarryPanozzo 7 жыл бұрын
If only university professors knew how to explain this intuitively and used animations like this.
@anilboppuri2067
@anilboppuri2067 5 жыл бұрын
we cannot compare, for creative students no explanation is required :)
@kbassols
@kbassols 3 жыл бұрын
Switching to online classes can help integratring this resources to our virtual courses :)
@Anriuko
@Anriuko 2 жыл бұрын
Somebody has to create the animations and somebody else has to pay for the time spent, and the professor's explanation would still be a garbled mess.
@arjunkc3227
@arjunkc3227 9 ай бұрын
He was taught by the professor. Some students grab what professor means and some lazy dont. Student have to be creative. Professor shows where the pond is. He doesnt force you to drink the water. Its upto you to drink or not. If its dirty water its you to clean little bit before you drink
@prabhusingh7481
@prabhusingh7481 6 жыл бұрын
Your videos make understanding and reasoning of difficult mathematical concepts so intuitive that it re-ignites passion for learning more. Thank you so much for taking the time to make these wonderful videos which help us grasp difficult concepts and make the learning experience so enjoyable.
@MrAxelx19
@MrAxelx19 5 жыл бұрын
You just explained to me in 4min what a semester of linear algebra couldn't
@Dr.Funknstein
@Dr.Funknstein 2 ай бұрын
Somehow went through an entire computer science degree without understanding what Eigenvectors and Eigenvalues are but in my defence no professor or KZbin lecture ever explained the concept this well.
@melontusk7358
@melontusk7358 4 жыл бұрын
Thanks so much, pal. Matrix Algebra has always scared me but this explanation and its applications to particles were really subtle and elegant. By the way, your voice is so calming that you gave me more confidence in the subject. This video should have a million views as it deserves more attention, and you just earned another subscriber.
@darshanprakash4143
@darshanprakash4143 5 жыл бұрын
dude after studying linear algebra for the past 10 years.....today i understood eigen vectors and eigen values
@antoniomaria4096
@antoniomaria4096 4 жыл бұрын
Its amazing how people from different origins, educations and country's all share the same thought "I have a diploma but i never really understood this subject properly until this video". This should make educators thing seriously about their methods and objectives.
@albertbatfinder5240
@albertbatfinder5240 3 жыл бұрын
This was brilliant. Practical visual example, and not a word wasted. Every other professor writes up four lines of formal definition, and basically explains nothing.
@MatTags3
@MatTags3 7 жыл бұрын
This was very helpful. My son just explained Eigen values and vectors to me on paper, which he did very well. Having your excellent video and graphics to watch next helped a ton. Well done! Thank you.
@adminassistant4409
@adminassistant4409 8 жыл бұрын
In 4 min, I just learned what an eigenvector is. Why did my teacher take 3 hours to teach us this? and why didn't I learn anything in those 3 hours!? Great explanation! So, it seems that eigenvectors can only be used on linear vectors, since the line can only be stretched and not moved around, right? So, what about those points and lines that move around...what are those called?
@LeiosLabs
@LeiosLabs 8 жыл бұрын
To be clear, we are transforming individual points and depicting the vectors as lines between them. We could have had the eigenvectors anywhere else on the plane, it just made sense to have them all go through the origin for visualization purposes. The ones that moved are just ordinary vectors (I don't think they have a special name). Any vector that is not an eigenvector will move around in a similar manner. I hope it helped!
@Antonio-lt1sp
@Antonio-lt1sp 3 жыл бұрын
90%+ teachers are just very bad at explaining things, in my limited experience.
@ravinishachincholkar358
@ravinishachincholkar358 6 жыл бұрын
Thank you soooooo much man, finally I am able to understand meaning of eigen vector, I have an exam tomorrow and no matter how many books I read, I wasn't able to understand the concept of eigen vector, you don't know how much your video has helped me, thanks once again, great video!!! You are the best teacher ever!!!!
@LeiosLabs
@LeiosLabs 6 жыл бұрын
I'm glad it was useful! This is one of the few cases where a clear visualization helps more than any book.
@bowlineobama
@bowlineobama Жыл бұрын
What a video!! Wow, Wow, Wow!! I have taken a linear algebra during my engineering degree back in 1986 and only now I understand what eigenvectors and eigenvalues are. Thanks.
@CrystalStarlight95
@CrystalStarlight95 7 жыл бұрын
A definition was exactly what I needed! I'm in linear algebra and this helps understand a bit of what's happening.
@gracialonignasiver6302
@gracialonignasiver6302 6 жыл бұрын
After a semester of Linear Algebra I could find Eigen Values/Vectors but never fully understood what they were. Your explanation is the best I've ever heard. I now have an actual idea of what I'm dealing with.
@LeiosLabs
@LeiosLabs 6 жыл бұрын
Thanks! I am glad it was useful!
@KingFredrickVI
@KingFredrickVI 8 жыл бұрын
Finally! You haven't uploaded in forever! This is a really nice video man :D good job. Explained it pretty well I think.
@LeiosLabs
@LeiosLabs 8 жыл бұрын
Thanks! I will try to get more videos out in the future. I have a plan for one every other week, but we'll see how that goes...
@curiash
@curiash Жыл бұрын
One of the best video on intuitive explanation of eigenvector.
@uroko2993
@uroko2993 8 жыл бұрын
Cool! According to my understanding, matrix, in certain circumstance, can be treated as a selection mechanism. When you apply the multiplication between specific matrix, for example, A, and vectors in different directions, some of the vectors will show a specific property, under which they only change in magnitude without swaying from their original direction(including the opposite way). These vectors are known as the "Eigenvector".
@LeiosLabs
@LeiosLabs 8 жыл бұрын
Yup, that's exactly right! =)
@eric321ification
@eric321ification 6 жыл бұрын
Dude...DOOOOD that is the best description I have heard of an eigenvector.
@LeiosLabs
@LeiosLabs 6 жыл бұрын
Dude...DOOOOD I'm glad you found it useful! =)
@Tweeteketje
@Tweeteketje 2 жыл бұрын
Wow!!! Such a clear explanation of the concept in just 4 minutes! That's really amazing ^^
@whomisac4616
@whomisac4616 7 жыл бұрын
This is the best clear explanation I got so far. Wish I had a tutor that could explain that in simple word while doing that calculus course. Anyway, I passed the course and doing multi-variable calculus course. Great videos.
@insideabrain2237
@insideabrain2237 3 жыл бұрын
This channel is pure gold. thank you for sharing your understanding with us!
@MrSunny9897
@MrSunny9897 7 жыл бұрын
This is the first time I really understand the meaning of eigen vector and eigen value. Great explanation dude.
@LeiosLabs
@LeiosLabs 7 жыл бұрын
I'm glad it was helpful!
@RaigyoEcU
@RaigyoEcU 3 жыл бұрын
Thanks, i always comeback to your channel at some point,years ago for verlet integration, now for eigen vectors that i need for some small derivations in epipolar geometry
@LoserHands
@LoserHands 4 жыл бұрын
The illustration was awesome!
@renes.234
@renes.234 7 жыл бұрын
Holy sh*t, thank you very much
@madannikalje760
@madannikalje760 6 жыл бұрын
Simple awesome actually accidentally I found this Channel and now I am so happy af
@GlenvandenBergen
@GlenvandenBergen 8 жыл бұрын
Perfect. This concept finally "clicked" for me.
@LeiosLabs
@LeiosLabs 8 жыл бұрын
Great! Glad to hear it! It honestly took me a long time to figure this stuff out because it's not presented explicitly in many places.
@BryceDoesLife
@BryceDoesLife 4 жыл бұрын
I'm a 4th-year computer science student and this is the best explanation I've ever heard. edit: spelling
@HarshShah-yt6tw
@HarshShah-yt6tw 8 жыл бұрын
Very well explained compared to other videos which just explains mechanical way of finding the eigen values and eigenvector... Keep it up!
@Helmutandmoshe
@Helmutandmoshe 6 жыл бұрын
This is the best short summary I've found on KZbin. Most linear algebra courses just bury the root meaning and it becomes obscured by the rote memorization of the algorithm. Thank you for this. You should do a more comprehensive conceptual explication of linear algebra concepts... it is much much needed. Three Blue one Brown has a very good series but your explanations are actually better. More insight.
@baluvnk8726
@baluvnk8726 4 жыл бұрын
I had seen some videos regarding this Eigen vectors but this video clears my idea . Thank you.
@LeiosLabs
@LeiosLabs 4 жыл бұрын
Glad it helped
@ChocooWafeer
@ChocooWafeer 6 жыл бұрын
Great video, short and informative. The animation really helped me understand what the eigen vectors do, from geometrical perspective. Thank you very much!
@LeiosLabs
@LeiosLabs 6 жыл бұрын
No problem! I'm glad you found it helpful!
@snehashishpaul2740
@snehashishpaul2740 6 жыл бұрын
Lucky me that I found this video that explained the concept mathematically supported with the help of 3d visualization. Great work
@worldrunner6420
@worldrunner6420 4 жыл бұрын
I literally have Differential Equations & Linear Algebra test this afternoon, and now I feel much more prepared for theory questions about these. Thanks!
@kinshuk0109
@kinshuk0109 4 жыл бұрын
Excellent Sonia....A great message put with conviction
@ammart-ws9qk
@ammart-ws9qk 6 ай бұрын
underrated one Now i just completly understand after searching a lot around 5 months
@BloomingBiz_Media
@BloomingBiz_Media 2 жыл бұрын
Bless your heart for the great visual
@6thHorseMan
@6thHorseMan 7 жыл бұрын
Thank you for the clear explanation. I was not aware that eigen vectors only stretched. Excellent visualization.
@LeiosLabs
@LeiosLabs 7 жыл бұрын
Yeah, it's one of the weird things that I only really understood after this visualization.
@JPLodine
@JPLodine 4 жыл бұрын
Beautifully simple. Thanks!
@joec8956
@joec8956 7 жыл бұрын
thanks! that was the clearest and most concise explanation I've found so far.
@LeiosLabs
@LeiosLabs 7 жыл бұрын
I'm glad it was helpful!
@spareful97
@spareful97 5 жыл бұрын
Quick, easy and straight to the point, this video deserves a like, and my professor deserves a smack on his bald spot.
@CyanKash
@CyanKash 4 жыл бұрын
I've been struggling to grasp this for 3 semesters but finally understand, thank you!
@santiagocanepa9099
@santiagocanepa9099 5 ай бұрын
First explanation that actually nails it!! THANKS
@DavidRoigCollell
@DavidRoigCollell 4 ай бұрын
Your explanation is incredibly clear. Thank you!!
@smie1250
@smie1250 4 жыл бұрын
This is super helpful and make more sense to learn eigenvalue and eigenvector! Thank you!
@amrits7939
@amrits7939 6 жыл бұрын
That was such a good and practical explanation.. i was trying to understand why is it so important from quite sometime!! Thanks Leios..
@LeiosLabs
@LeiosLabs 6 жыл бұрын
I'm glad it was helpful!
@twoboxtoofurious
@twoboxtoofurious 7 жыл бұрын
this is awesome. I have already studied this and forgotten, but this really helped me remember.
@finalkamen
@finalkamen 7 жыл бұрын
Planning to learn quantum mechanics by myself! This "quick expert" explanation may the useful entry guide for me :p
@LeiosLabs
@LeiosLabs 7 жыл бұрын
Quantum Mechanics is super difficult to learn (especially on your own). I would suggest learning a good bit of mathematics (including linear algebra and differential equations) and then attacking Introduction to Quantum Mechanics by Griffiths; however, there might be better books out there!
@finalkamen
@finalkamen 7 жыл бұрын
Thank for the suggestions, bro! Actually, I have the "Feynman Lectures on Physics" in my collection of textbooks. I came from engineering background, but have deep interesting on pure physics thought (y)
@mohitpandey585
@mohitpandey585 6 жыл бұрын
Thank you so much, it helped me a lot in understanding PCA.
@LeiosLabs
@LeiosLabs 6 жыл бұрын
I'm glad it was useful!
@sdog7334
@sdog7334 6 жыл бұрын
I spent 2.5 years in college wondering wtf an eigenvalue and eigenvector is and just learned it within 4 minutes of watching this video. Ask me if I'm pissed.
@LeiosLabs
@LeiosLabs 6 жыл бұрын
Are you pissed?
@shivipurwaha292
@shivipurwaha292 6 жыл бұрын
Simple, crisp explanation with amazing visualization. Thank a lot.
@AmlanPanigrahi
@AmlanPanigrahi 5 жыл бұрын
I came here because of my quest to understand PCA algorithm which is used in unsupervised learning. Awesome explanation.
@rebeccaschley5146
@rebeccaschley5146 6 жыл бұрын
This was very helpful to my understanding of their role in dimensionality reduction. Thank you!
@LeiosLabs
@LeiosLabs 6 жыл бұрын
Cool! I'm glad it was useful! Good luck!
@ash6215
@ash6215 7 жыл бұрын
Wow finally i understood what Eigen vectors are , thanks :)
@lionelward1762
@lionelward1762 7 жыл бұрын
brilliant!!! this way of looking at eigenvectors and eigenvalues is completely new to me, and extremely helpful
@greenb1a
@greenb1a 2 жыл бұрын
Excellent description both intuitively and mathematically
@BitcoinmeetupsOrg123
@BitcoinmeetupsOrg123 6 жыл бұрын
Awesome man!!!!!!! I have wondered for some time how to understand eigenvectors. Trying to learn more about matrix multiplications, convolutions, gradient descent and stuff like that too!
@LeiosLabs
@LeiosLabs 6 жыл бұрын
I'm glad ti was helpful! It's easy to understand certain things once they are appropriately visualized.
@merp1998
@merp1998 8 жыл бұрын
2 things: 1. You are so cute! 2. The explanation was really good. My only problem was 2:37 - 2:50. The animation was quick so it was hard to fully appreciate the point you were trying to make, but I think the subsequent animation explained it. Cheers :)
@LeiosLabs
@LeiosLabs 8 жыл бұрын
Thanks! I'm glad you enjoyed the video. The animation was rather quick. Looking at it now, I should have slowed it down and really stressed the fact that every single point in the cube represents a position vector that we are transforming. That said, I show the transformation a few times and think that's enough for most people. peace =)
@rishabhjain1470
@rishabhjain1470 7 жыл бұрын
Hey man !! thanks a lot for putting this up. Its one of the very few videos that explain it with 3D visualization !! thanks a lot , subscribed
@LeiosLabs
@LeiosLabs 7 жыл бұрын
I'm glad you liked it / it was useful!
@amrahmad3536
@amrahmad3536 7 жыл бұрын
Thank you very much, I think this is the best explanation for the eigenvalues and eigenvectors.
@LeiosLabs
@LeiosLabs 7 жыл бұрын
I am glad it was useful!
@Thevboy97
@Thevboy97 8 жыл бұрын
that's a really nice explanation....especially concerning the physical aspect of eigenvectors
@LeiosLabs
@LeiosLabs 8 жыл бұрын
Yeah, it's not the easiest thing to understand when it's hidden behind odd notation.
@solaokusanya955
@solaokusanya955 Жыл бұрын
Where have you been all my life!!!... You have conquered it all!.. Thank you!!
@richardspitzer6060
@richardspitzer6060 3 жыл бұрын
Great explanation. Just wondering now where the eigenvector is used and why it is important. Adding these explanations to the video would complete the video in my opinion. Thanks for the effort!
@LarmoyanteLamentierlust
@LarmoyanteLamentierlust 4 жыл бұрын
Very clear and easy to understand, thank you very much! I feel like I finally have a grasp on what these terms mean, after having heard of them many times, but never really understood.
@bartonpaullevenson3427
@bartonpaullevenson3427 4 жыл бұрын
Short, sweet, and to the point. Very well presented. Thanks!
@zaynumar0
@zaynumar0 6 жыл бұрын
THANK YOU SO MUCH LEIOS , IT MADE MAKING REVISION OF MATRICIES AND EIGENVALUES MUCH MORE INTUATIVE AND ENJOYABLE !!! :) :) :)
@kevinlin4157
@kevinlin4157 7 жыл бұрын
Very good explanation that help me understand, in some way Eigenvector explains the direction of things. It doesn't matter how it transform linearly by applying magnitude, it will always go to the same direction but some case stretch.
@RaymondLee1220
@RaymondLee1220 6 жыл бұрын
I learned more in this video than 2 hours of lecture from my professor
@LeiosLabs
@LeiosLabs 6 жыл бұрын
I'm glad it was helpful!
@alwysrite
@alwysrite 7 жыл бұрын
great explanation and good animation to go with it- gives me a solid understanding
@shariqueahmed5106
@shariqueahmed5106 6 жыл бұрын
great!! it was difficult for me to visualize it at first, but explained it very simple way
@LeiosLabs
@LeiosLabs 6 жыл бұрын
Yeah. I am glad it was helpful!
@JulesCalella
@JulesCalella 7 жыл бұрын
Very useful. It's cool knowing the math and how it works, but physical or graphical examples really hit it home for me.
@LeiosLabs
@LeiosLabs 7 жыл бұрын
I'm glad it was helpful!
@sandeepsingh-ly9nh
@sandeepsingh-ly9nh 7 жыл бұрын
thankyou so, much. It was the best explanation, i have yet. Keep it up!!
@abdulrahmankerim2377
@abdulrahmankerim2377 7 жыл бұрын
This is the first time I get the physical meaning of Eigenvector :) Great thanks
@LeiosLabs
@LeiosLabs 7 жыл бұрын
I'm glad it was helpful!
@_Swink
@_Swink 7 жыл бұрын
Great video. Explained with simplicity and clarity!
@pragazv
@pragazv 8 жыл бұрын
simple effective and it was like what i expected... even a common man can understand..... grt... really great...
@youjjeuy9245
@youjjeuy9245 3 жыл бұрын
Thank you so much! This helped a lot even after 4 years :)
@CheckToTheMate
@CheckToTheMate 8 жыл бұрын
Thanks for the explanation man, it was a really great video!
@LeiosLabs
@LeiosLabs 8 жыл бұрын
I'm glad you liked it! =)
@DiegoDiaz-ir4nd
@DiegoDiaz-ir4nd 7 жыл бұрын
Best explanation EVER! Thank you!
@LeiosLabs
@LeiosLabs 7 жыл бұрын
I am glad it was useful! =)
@LyyrRATM
@LyyrRATM 8 жыл бұрын
I love this. Simple and clear. Bravo!
@LeiosLabs
@LeiosLabs 8 жыл бұрын
I'm glad it was helpful! =)
@FLMKane
@FLMKane Жыл бұрын
Aaaaand... Subscribed. Wish I had this video when I was taking Controls classes
@abdulazizalqallaf1704
@abdulazizalqallaf1704 6 жыл бұрын
BEST EXPLANATION EVER!
@LeiosLabs
@LeiosLabs 6 жыл бұрын
Thanks! I'm glad it was useful!
@astayonix
@astayonix 4 жыл бұрын
Phenomenal explanation! Extremely succinct and beautifully articulated!
@RansonJoe
@RansonJoe 8 жыл бұрын
Wow. That was explained so clearly. Terrific! :)
@newbskillerzzz
@newbskillerzzz 8 жыл бұрын
Good! Not sure i'll be applying it as a chemist, but still learned something today!
@LeiosLabs
@LeiosLabs 8 жыл бұрын
That's alright! I am glad you learned something!
@aumkarinamdar5181
@aumkarinamdar5181 4 жыл бұрын
Thanks a lot! A simple but clear explanation. Really appreciate this video.
@ffhashimi
@ffhashimi 8 жыл бұрын
This is really great and simple ; I am eager to watch more of your videos .. good job
@LeiosLabs
@LeiosLabs 8 жыл бұрын
I'm glad you liked it!
@g7plus69
@g7plus69 4 жыл бұрын
just awesome....great efforts for students and society with out expectations. Thank you
@NetMistro
@NetMistro 7 ай бұрын
The most beautiful explanation.
@jeanapp_
@jeanapp_ 8 жыл бұрын
Clear and simple. Thank you so much!
@ignite21385
@ignite21385 6 жыл бұрын
Best video on the internet today. Period.
@LeiosLabs
@LeiosLabs 6 жыл бұрын
I am glad you think so!
@gottlobfreige1075
@gottlobfreige1075 3 жыл бұрын
Much better explanation that the crazy Graph video in KZbin
@sandywu547
@sandywu547 2 жыл бұрын
Best explanation I've seen by far!
@GQElvie
@GQElvie 5 жыл бұрын
thank you very much for this explanation. wow. after many attempts, this is the best I have seen yet.
@azeemiqbal
@azeemiqbal 7 жыл бұрын
Oh! man such an easy explanation! May God Bless you!
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