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What is an Eigenvector? 

Leios Labs
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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.joshwoodward.com/
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

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24 июн 2016

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Комментарии : 679   
@lradmclovin9
@lradmclovin9 6 лет назад
You just ended years of confusion in 4 minutes. Thank you
@LeiosLabs
@LeiosLabs 6 лет назад
I'm glad it was helpful! =)
@danpal6737
@danpal6737 3 года назад
me too , but 2 years later, jobless and unmarried.....
@TheyHurry
@TheyHurry Год назад
Woah I didn't expect Bernie to be studying linear algebra
@snokful
@snokful Год назад
@@TheyHurry the pen is not as popular as the sword (sadly). but hopefully in the end, mightier.
@lararomao3786
@lararomao3786 Год назад
Yes ahaha
@yongyoon2157
@yongyoon2157 7 лет назад
Embarrassingly , I admit that finally I got some meaning in eigenvector and eigenvalue after all those years. Thanks for the insight.
@LeiosLabs
@LeiosLabs 7 лет назад
Don't worry, I think everyone knows that feeling! =)
@rickoshea9282
@rickoshea9282 6 лет назад
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 4 года назад
I couldn't agree with you more. FINALLY!
@itsnotallrainbowsandunicor1505
@itsnotallrainbowsandunicor1505 4 года назад
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 года назад
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.
@LarryPanozzo
@LarryPanozzo 7 лет назад
If only university professors knew how to explain this intuitively and used animations like this.
@anilboppuri2067
@anilboppuri2067 5 лет назад
we cannot compare, for creative students no explanation is required :)
@kbassols
@kbassols 3 года назад
Switching to online classes can help integratring this resources to our virtual courses :)
@Anriuko
@Anriuko 2 года назад
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 6 месяцев назад
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
@Louis412e
@Louis412e 8 лет назад
i'm a third year physics major and this was the best explanation i've ever seen, by far. good job!
@LeiosLabs
@LeiosLabs 8 лет назад
Thanks, man! I appreciate it!
@isakhammer6558
@isakhammer6558 4 года назад
same! Difficult subject though
@jessfairbairn4722
@jessfairbairn4722 6 лет назад
You're the first person to have successfully explained eigenvectors in a way I can visualise, so thank you!
@LeiosLabs
@LeiosLabs 6 лет назад
I'm glad it was useful!
@wrcz
@wrcz 4 года назад
I literally got chills over my spine from finally understanding. And it is so bloody simple! Thank you! Absolutely brilliant
@priyankaverma9668
@priyankaverma9668 7 лет назад
Wonderful explanation. The geometrical meaning of eigen vector is explained very well. ThankYou for such a nice explaination
@prabhusingh7481
@prabhusingh7481 5 лет назад
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.
@melontusk7358
@melontusk7358 3 года назад
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.
@MatTags3
@MatTags3 7 лет назад
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.
@whomisac4616
@whomisac4616 7 лет назад
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.
@curiash
@curiash Год назад
One of the best video on intuitive explanation of eigenvector.
@insideabrain2237
@insideabrain2237 3 года назад
This channel is pure gold. thank you for sharing your understanding with us!
@KingFredrickVI
@KingFredrickVI 8 лет назад
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 лет назад
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...
@Tweeteketje
@Tweeteketje Год назад
Wow!!! Such a clear explanation of the concept in just 4 minutes! That's really amazing ^^
@lionelward1762
@lionelward1762 7 лет назад
brilliant!!! this way of looking at eigenvectors and eigenvalues is completely new to me, and extremely helpful
@snokful
@snokful Год назад
Examiner (no live lectures any more) linked to this at start of course. Very helpful beginning. Thankyou. Gave me an appetite to understand more.
@HarshShah-yt6tw
@HarshShah-yt6tw 7 лет назад
Very well explained compared to other videos which just explains mechanical way of finding the eigen values and eigenvector... Keep it up!
@worldrunner6420
@worldrunner6420 4 года назад
I literally have Differential Equations & Linear Algebra test this afternoon, and now I feel much more prepared for theory questions about these. Thanks!
@CrystalStarlight95
@CrystalStarlight95 7 лет назад
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 лет назад
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 лет назад
Thanks! I am glad it was useful!
@_Swink
@_Swink 7 лет назад
Great video. Explained with simplicity and clarity!
@aeromateen6773
@aeromateen6773 5 лет назад
Whoa! Finally after my graduation, I understood the concept by just coming across the video randomly. 😂
@YT-bl8hs
@YT-bl8hs 6 лет назад
Very informative! This style of teaching video is the best for me more than captured computer screen.
@LeiosLabs
@LeiosLabs 6 лет назад
That was the goal! =)
@dr34mc4st3r
@dr34mc4st3r 7 лет назад
one of the best quick explanation of eigenvectors/eigenvalues yet!
@LeiosLabs
@LeiosLabs 7 лет назад
I'm glad it was useful!
@roshanshanmughan7218
@roshanshanmughan7218 5 лет назад
A great explanation. I've been trying to get the physical meaning of this stuff and you've given me just that. Thank you buddy!
@ChocooWafeer
@ChocooWafeer 6 лет назад
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 лет назад
No problem! I'm glad you found it helpful!
@zaynumar0
@zaynumar0 6 лет назад
THANK YOU SO MUCH LEIOS , IT MADE MAKING REVISION OF MATRICIES AND EIGENVALUES MUCH MORE INTUATIVE AND ENJOYABLE !!! :) :) :)
@sandeepsingh-ly9nh
@sandeepsingh-ly9nh 7 лет назад
thankyou so, much. It was the best explanation, i have yet. Keep it up!!
@shivipurwaha292
@shivipurwaha292 5 лет назад
Simple, crisp explanation with amazing visualization. Thank a lot.
@bartonpaullevenson3427
@bartonpaullevenson3427 4 года назад
Short, sweet, and to the point. Very well presented. Thanks!
@ravinishachincholkar358
@ravinishachincholkar358 6 лет назад
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 лет назад
I'm glad it was useful! This is one of the few cases where a clear visualization helps more than any book.
@kinshuk0109
@kinshuk0109 3 года назад
Excellent Sonia....A great message put with conviction
@RaigyoEcU
@RaigyoEcU 3 года назад
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
@amrits7939
@amrits7939 6 лет назад
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 лет назад
I'm glad it was helpful!
@astayonix
@astayonix 3 года назад
Phenomenal explanation! Extremely succinct and beautifully articulated!
@awaisahmad5908
@awaisahmad5908 3 года назад
Amazing demonstration. Sir you have cleared my concepts regarding eigenVector
@LarmoyanteLamentierlust
@LarmoyanteLamentierlust 4 года назад
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.
@albertbatfinder5240
@albertbatfinder5240 2 года назад
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.
@bowlineobama
@bowlineobama Год назад
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.
@uroko2993
@uroko2993 7 лет назад
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 7 лет назад
Yup, that's exactly right! =)
@nurman2011
@nurman2011 6 лет назад
Seriously, this is the best explanation ever. Can't wait to see your other videos.
@LeiosLabs
@LeiosLabs 6 лет назад
I'm glad you liked it!
@rishabhjain1470
@rishabhjain1470 7 лет назад
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 лет назад
I'm glad you liked it / it was useful!
@jdmphys3040
@jdmphys3040 7 лет назад
I found this explanation so helpful. I thought breaking apart the mathematical and physical perspectives made it so clear, and so did the simple examples. Thank you!!!!
@LeiosLabs
@LeiosLabs 7 лет назад
I'm glad it was helpful! =)
@MrAxelx19
@MrAxelx19 4 года назад
You just explained to me in 4min what a semester of linear algebra couldn't
@DavidRoigCollell
@DavidRoigCollell Месяц назад
Your explanation is incredibly clear. Thank you!!
@LoserHands
@LoserHands 4 года назад
The illustration was awesome!
@BloomingBiz_Media
@BloomingBiz_Media 2 года назад
Bless your heart for the great visual
@taoli2635
@taoli2635 7 лет назад
Very cool explanation especially the visual demo of the geometrical meaning of eigen vector. Thanks for sharing the video!
@LeiosLabs
@LeiosLabs 7 лет назад
I'm glad it was useful!
@ven7782
@ven7782 4 года назад
I went through a bunch of stuff like khan academy, wolfram etc but this explanation was by far the most intuitive.
@kevinlin4157
@kevinlin4157 7 лет назад
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.
@BitcoinmeetupsOrg123
@BitcoinmeetupsOrg123 6 лет назад
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 лет назад
I'm glad ti was helpful! It's easy to understand certain things once they are appropriately visualized.
@darshanprakash4143
@darshanprakash4143 5 лет назад
dude after studying linear algebra for the past 10 years.....today i understood eigen vectors and eigen values
@andynkili672
@andynkili672 Год назад
Best and simplest explanation that I have ever heard! Thank you
@ozzyfromspace
@ozzyfromspace 5 лет назад
You just gave me an idea about a math problem in number theory I'm working on..... Thanks, and nice video (lol I needed the refresher).
@smie1250
@smie1250 4 года назад
This is super helpful and make more sense to learn eigenvalue and eigenvector! Thank you!
@joec8956
@joec8956 7 лет назад
thanks! that was the clearest and most concise explanation I've found so far.
@LeiosLabs
@LeiosLabs 7 лет назад
I'm glad it was helpful!
@sacredsoma
@sacredsoma 4 года назад
Gratitude for such a lucid explanation. I salute your effort
@alwysrite
@alwysrite 7 лет назад
great explanation and good animation to go with it- gives me a solid understanding
@tamizhtamizh412
@tamizhtamizh412 4 года назад
U guys are seriously the best ❤
@RansonJoe
@RansonJoe 8 лет назад
Wow. That was explained so clearly. Terrific! :)
@wizardOfRobots
@wizardOfRobots 6 лет назад
Hi LeiosOS, that was a great explanation witha really cool video. Just found your channel and loved it. Love from India.
@louxan9055
@louxan9055 6 лет назад
Clear, very clear! And thank you also for speeding up the video while writing on the blackboard!
@LeiosLabs
@LeiosLabs 6 лет назад
I'm glad it was helpful! I make sure that video matches the audio.
@twoboxtoofurious
@twoboxtoofurious 7 лет назад
this is awesome. I have already studied this and forgotten, but this really helped me remember.
@baluvnk8726
@baluvnk8726 4 года назад
I had seen some videos regarding this Eigen vectors but this video clears my idea . Thank you.
@LeiosLabs
@LeiosLabs 4 года назад
Glad it helped
@adminassistant4409
@adminassistant4409 8 лет назад
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 лет назад
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 года назад
90%+ teachers are just very bad at explaining things, in my limited experience.
@CyanKash
@CyanKash 3 года назад
I've been struggling to grasp this for 3 semesters but finally understand, thank you!
@antoniomaria4096
@antoniomaria4096 4 года назад
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.
@NicturnalBeats
@NicturnalBeats 2 года назад
I love you Leios, good job.
@Helmutandmoshe
@Helmutandmoshe 5 лет назад
This is the best short summary I've found on RU-vid. 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.
@garrytalaroc
@garrytalaroc 7 лет назад
First video from you, and I just subscribed, great video, learned a lot, thanks.
@LeiosLabs
@LeiosLabs 7 лет назад
I'm glad it was helpful!
@ffhashimi
@ffhashimi 8 лет назад
This is really great and simple ; I am eager to watch more of your videos .. good job
@LeiosLabs
@LeiosLabs 8 лет назад
I'm glad you liked it!
@santiagocanepa9099
@santiagocanepa9099 2 месяца назад
First explanation that actually nails it!! THANKS
@CheckToTheMate
@CheckToTheMate 8 лет назад
Thanks for the explanation man, it was a really great video!
@LeiosLabs
@LeiosLabs 8 лет назад
I'm glad you liked it! =)
@burhanorfali
@burhanorfali Месяц назад
Your work is amazing my friend. Thank you ❤❤
@JanakaWij
@JanakaWij 6 лет назад
Your videos are awesome! Keep up the good work sir!
@LeiosLabs
@LeiosLabs 6 лет назад
I'm glad you like the videos!
@abhinavchauhan2737
@abhinavchauhan2737 7 лет назад
Wow ! Thanks man...both your theoretical & geometrical explanations are spot on !!!
@richardspitzer6060
@richardspitzer6060 3 года назад
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!
@MrSunny9897
@MrSunny9897 7 лет назад
This is the first time I really understand the meaning of eigen vector and eigen value. Great explanation dude.
@LeiosLabs
@LeiosLabs 7 лет назад
I'm glad it was helpful!
@youjjeuy9245
@youjjeuy9245 3 года назад
Thank you so much! This helped a lot even after 4 years :)
@Youcanscienceit
@Youcanscienceit 8 лет назад
Thanks so much. I've been struggling with this concept, largely due to the way the language is used (darn german words in physics). Especially the geometric visualization. I'd seen the matrix multiplication sort of example before but tying it to the visual of the transform was super helpful. Keep it up.
@LeiosLabs
@LeiosLabs 8 лет назад
Thanks, man! I am the same way. Without seeing the cube physically changing shape, eigenvectors were "mathemagic" to me!
@y.z.6517
@y.z.6517 6 лет назад
Eigenvector means own vector.
@JPLodine
@JPLodine 4 года назад
Beautifully simple. Thanks!
@aumkarinamdar5181
@aumkarinamdar5181 4 года назад
Thanks a lot! A simple but clear explanation. Really appreciate this video.
@gandalfs_goat
@gandalfs_goat 7 лет назад
Fantastic explanation! Very well done, thank you.
@LyyrRATM
@LyyrRATM 7 лет назад
I love this. Simple and clear. Bravo!
@LeiosLabs
@LeiosLabs 7 лет назад
I'm glad it was helpful! =)
@GQElvie
@GQElvie 5 лет назад
thank you very much for this explanation. wow. after many attempts, this is the best I have seen yet.
@eric321ification
@eric321ification 6 лет назад
Dude...DOOOOD that is the best description I have heard of an eigenvector.
@LeiosLabs
@LeiosLabs 6 лет назад
Dude...DOOOOD I'm glad you found it useful! =)
@horotat
@horotat 5 лет назад
Really nice, concise, and clear explanation. Thank you.
@ash6215
@ash6215 7 лет назад
Wow finally i understood what Eigen vectors are , thanks :)
@dibbsm7243
@dibbsm7243 5 лет назад
You have changed the game this made so much sense!!! Ty
@sandywu547
@sandywu547 2 года назад
Best explanation I've seen by far!
@rebeccaschley5146
@rebeccaschley5146 6 лет назад
This was very helpful to my understanding of their role in dimensionality reduction. Thank you!
@LeiosLabs
@LeiosLabs 6 лет назад
Cool! I'm glad it was useful! Good luck!
@g7plus69
@g7plus69 3 года назад
just awesome....great efforts for students and society with out expectations. Thank you
@techtana9268
@techtana9268 6 лет назад
This is the greatest visualization of eigenvalues!
@maycolmedina6074
@maycolmedina6074 5 лет назад
Excelente, breve y conciso, como debe ser.
@asadurrahman1563
@asadurrahman1563 7 лет назад
Boss, you are great. This video makes my thought clearer that before.... Thank you
@snehashishpaul2740
@snehashishpaul2740 5 лет назад
Lucky me that I found this video that explained the concept mathematically supported with the help of 3d visualization. Great work
@azeemiqbal
@azeemiqbal 7 лет назад
Oh! man such an easy explanation! May God Bless you!
@madannikalje760
@madannikalje760 5 лет назад
Simple awesome actually accidentally I found this Channel and now I am so happy af
@shariqueahmed5106
@shariqueahmed5106 6 лет назад
great!! it was difficult for me to visualize it at first, but explained it very simple way
@LeiosLabs
@LeiosLabs 6 лет назад
Yeah. I am glad it was helpful!
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