The applications of eigenvectors and eigenvalues | That thing you heard in Endgame has other uses
ฝัง
- เผยแพร่เมื่อ 12 ธ.ค. 2019
- Get free access to over 2500 documentaries on CuriosityStream: go.thoughtleaders.io/112852019... (use promo code "majorprep" at sign up)
STEMerch Store: stemerch.com/
Support the Channel: / zachstar
PayPal(one time donation): www.paypal.me/ZachStarYT
This video covers the applications of eigenvectors and eigenvalues (in and outside of mathematics) that I definitely didn't learn in school.
Follow me on Instagram: / zachstar
Twitter: / imzachstar
Join Facebook Group: / majorprep
The applications of matrices: • The Applications of Ma...
The PageRank Algorithm: • The algorithm that sta...
Desmos (software used in video): www.desmos.com/calculator
►My Setup:
Space Pictures: amzn.to/2CC4Kqj
Magnetic Floating Globe: amzn.to/2VgPdn0
Camera: amzn.to/2RivYu5
Mic: amzn.to/2BLBkEj
Tripod: amzn.to/2RgMTNL
Equilibrium Tube: amzn.to/2SowDrh
►Check out the MajorPrep Amazon Store: www.amazon.com/shop/zachstar
![TREASURE - 'KING KONG' COMEBACK SPECIAL [THE TREASURE SHOW]](http://i.ytimg.com/vi/Jx1wyMaQzf0/mqdefault.jpg)
You touched on linear algebra, differential equations, and probability/statistics, three of the four areas of math that underlie most engineering and computing applications today (the fourth being number theory.) Nice video.
What about graph theory?
also zombies
Imgay Asheck that can somewhat fall under linear algebra since there’s matrix multiplication involved
I'm soooooo confused 🤪
@@imgayasheck595 Graph Theory is more or less a part of Linear Algebra, since a graph can be represented as a matrix
You and grant Sanderson are the reasons my interest in "understanding" mathematics is still alive ... I just can't express in words how much I owe to you both 🙏🙏🙏huge respect from India
Same
You should also know Mathologer.
How's the progress going on, Shama ji?
It's a bit sad because you need someone (other than yourself) to cultivate curiosity towards math
Aww yes ! That feeling when you just finished your masters in computer science and everything on this video made perfect sense.
sana ol nakapag masteral
🤩 I just got my Masters. 😂
@@jj74qformerlyjailbreak3 nice
@@cruzmarco6048 Nothing but ❤️ my friend. 👍
Chi chi would be proud
This was a better explanation in 20 minutes than anything in my Diff Eq + Lin Alg class. I just finished a test on eigenmagic with a decent grade, and I didn't know what an eigenvalue even was.
Great quote from the video, “Eigenvectors/Eigenvalues (in many cases) reveal long term behavior.” Why is this not the leading sentence for every math class discussing this topic? All of the sudden its application became extremely clear.
So, I'm from Uruguay (Our native language is Spanish), and I was hearing the video (Started with a related one, of the same channel) and thought: "Ok, eigenvalues, and eigenvectors are really cool! So why I'm not learning this at University?", And I searched the translation, that is: "Valores propios, y Vectores propios" respectively.
I'm shock.
I have been calculating the eigenvalues, and the dimensions of the subspaces associated, all over the place, but no one has ever teached us what the hack they are used for!
Yeah... I'm probably dumb because I didn't searched about this before, and, I know, some times is hard to teach "all the aplications" of an unknown tool, (for the studient). But, is just far more engaging and useful to understand why i'm using "det(A-xI)" and solving a weird polinomium.
Anyways. Thank you SO much, for the video.
Autovectores y autovalores se suele usar en los libros de texto en español también
This is very true. In physics, and especially in Quantum Mechanics we use eigenvectors/values all the time. It's really fundamental - but my course (many, many years ago) never once covered what they are geometrically or even in some depth mathematically. They were simply presented as a series of algebraic manipulations of arrays of numbers to get 'the answer'.
To this day, even though I can calculate the probability amplitude of spin states of electrons (for example) I haven't the faintest idea why this model works as it does and how it came to be invented in the first place.
Dec 12:
Me: finishes finals for differential equations and linear algebra.
Dec 13.
Major Prep: Eigenstuff
Me: well, the timing couldn't have been better
Since we talked about the google page rank algorithm it seems fit to tell you that your exam probably caused you to be here :)
No joke, your content has singlehandedly revived my interest and passion for pursuing both learning and teaching math and algorithms. I’m going to really, finally, put my nose to the grindstone to cop an ICPC medal off this inspiration high. You’re the best, Zach, and you have a new Paterson member. Godspeed!
Dude what a donation! Seriously appreciate it and hope you go pursue those interests and passions, best of luck!
Love your videos Bro.. in an age where school is killing interest in the sciences, your videos keep my curiosity and interest alive... ❤️❤️
Sukalyan Roy truf
School isn't killing interest in sciences. It just fails to keep up/compete with the insane amount of interactive, appealing and sometimes addictive content available online.
Daily life is THE perpetual school of sciences, be it material science (build a house, make a dress), math science (budget, electricity), language science (talk to your neighbor of dissimilar roots) or history science (voting), and only peer pressure is killing interest in being interested, therefore you, alone, are responsible for keeping your interests alive. I'm sure you will go far, maybe one day you will be in a position to direct the interests of other, to catch someone who is falling to peer pressure and show them the benefit of joining you in the journey.
@@b_kind force-feeding subjects instead of giving insights about applications is a frequently complained part of schools though, even on subjects that are very useful. That probably contributed to the "killing"
You said it, I can say first-hand that my highschool is ruining science and especially math for the majority of students, it's truly a shame
Dawn, you can turn yourself into an engineer just by watching this and other few channels on youtube (believe me, I'm an engineer). It's so well explained and easy to understand that makes real classes tiring and boring. Thank you so much for spending your time making those helpful videos!
I don't know bro, you gotta do a lot of exercises haha
I am not in college, but videos like this is rekindling my interest in mathematics, which I love more than crosswords.
@@BooyahLThat's true, but most of the concepts you can find here on youtube, even some applications/projects and advanced exercises. I know it doesn't replace a real engineering course, but there are so many things that you find here on youtube that if you had a guide of what to study next, you would have a pretty good idea of what is a engineering course.
@@RM-zx9ee And if you just start zooming around Wikipedia pages on math, you could learn a lot... more than you could possible absorb all of.
I used to think that too but lately I’ve changed my stance. Learning is iterative and I think what makes videos like these so good is normally because this isn’t your first pass over the subject
Having watched all the previous videos, this one felt a lot like a sequel and I simply loved it. As a Math teacher having to teach Linear Algebra to engineering students, your videos are a great source of inspiration! Thank you!
I just took my linear algebra final, and this video answers the question my professor failed to all semester: what is the point of all these techniques I'm learning?
So true. I feel the exact same way. I wish math classes would include more material on application.
Why are you studying maths if this is a question you care about?
@@SpaghettiToaster I'm a computer science major, and this is a requirement. If I wanted to study something for it's inherent beauty, I'm be a liberal arts major.
@The Thunderblade Damn dude, I was joking, but where at all did I say say anything approaching "what is maths?"
Regardless of the subject, a student's going to grasp the material better with some understanding of context. For example, Mondrian's famous abstract art seems pretty simple if you see it out of context (you know, the ones with the thick black lines and geometric shapes in primary colors), but when you appreciate what the guy was able to do earlier in his career, and why he chose to go abstract instead, it lends a better understanding of why his art is so impactful.
Check it out, I have no problem with learning advanced maths. My issue arises when I, along with a good chunk of my class, were asking in good faith, "what do these numbers we're coming up with mean?" I get that there are people who enjoy doing math just to see the formulae churn out answers, as that's who my LA professor was, but it's not me. This guy was teaching at a superficial level of just showing us various techniques without bothering to give us any insight into the larger implications of what the math meant, and it made the course more of a headache than it needed to be.
Maybe go talk to someone about unleashing that kind of hostility on a total stranger, though. Can't be good for you to carry around that level of vitriol.
@@SpaghettiToaster I thought the question quite valid and mirrored my own when reflecting upon how and why the curriculum I followed was created. There must have been a perceived context within which what was to be taught was decided. As an example, although I did Linear Algebra we didn't touch upon Eigen 'stuff', however in a Numerical Analysis we were shown how to calculate the eigenvalues of n-dimensional matrices. I did wonder why. It was only after I graduated and taught myself Quantum Mechanics, starting with The Copenhagen interpretation that I came across Eigen 'stuff' and the penny dropped as to why. Mathematics in and of itself is beautiful but in a course created by a random subset of planetary mathematicians it can be useful to know the why because that hints towards the collective understanding of the Department's research staff and 'the arrow' of their vision. One always be brave enough to ask 'why' and not just settle for being told.
When the eigenvalue is imaginary, that means you got out of R² , and the eigenvector is perpendicular to the plan, that is the 3D vector [ 0 0 1 ], it's actually the rotation axes for the 2D rotation, that's our eigenvector in that case..., this also happens when solving vectors in 1D and getting the value “i” as result, that's actually the vector [ 0 1] in 2D => the vector perpendicular to the subspace we are in
(+newdhia hassen) Got it. Kind of like curl.
Thanks, that was helpful. :)
I was thinking in similar lines since the imaginary plane is just the other plane of physical value that affects the current observed value we are dealing with. it's just in a different plane. Nice one.
oooh
That's a nice interpretation.
Been binge-watching your transformation video. Although i've done my signal processing course (which i suck at), your video gave me new insights on how to look at those transformations, big thanks! :D
Feedback: The last videos have been awesome! They speak to the intuition, and allow people a much better understanding of how things work and when they apply. You've done a fantastic job - thank you for doing it. This is the kind of video people should keep returning to until the info it contains stick - it is integral to understanding pretty much any complex system. This really helps! 👍
This is great! Thank you! Glad to be your Patreon supporter and to be able to see your videos first!
Thanks for the continued support Nick! Glad to keep seeing you in the comments
This was really helpful. I'm watching several videos on eigenvectors and eigenvalues right now because I did have this stuff in college, but back then, it wasn't well explained as it is with the animations you roll back and forth. I really appreciate this. Thank you.
Damn, I didn't know this when we learned this. They should have told us this first.
you weren't ready. And you would have complained anyway.
@@donegal79 Aren't we all not ready for what school is going to teach us? Should we go through the entire textbook before attending the first lesson?
I had the pleasure of being directed to your videos today. Thank you tech companies (who paid attention in Linear Algebra classes) for using what I suspect to be a low-rank matrix decomposition to learn about my viewing preferences.
Wow, this was huge. The simple explanation you started with got me to get all excited every time I saw the eigenvectors coming up! Really nicely done!
I had a brilliant doctoral computer science professor this semester and he pretty much told us that physicists and engineers he collaborated with over his career most of the time wanted fast ways to solve for eigenvalues on large computer systems lol
Thanks you very much, this completely boosted my understanding after studying this a year ago and not knowing any practical applications or even the essence of studying and understanding them...i'm grateful for time and effort you took to make such a clear video...
We spent like 2 weeks learning about these in my math paper, I had no idea what any of it was about, but at least I could do the arithmetic. This video's visual explanation is soo much better for understanding what these are than any math text book
Thanks man. You have my respect. I have taken courses on linear algebra in my college, but the way you explain won my heart. This motivates me to learn about it more, whereas the studies in college were mostly numerical and boring. Thanks for all knowledge you are contributing to this world! Keep making such videos. I love your channel.
This is an excellent demonstration. I've been struggling with the concept of the Eigenvector for some time and have explored many sources for different explanations. This is by far the best, I think I may almost understand their purpose now. Please keep up the good work!
love it -- excellent explanations (just the right level/speed), and a fantastic compilation of the best examples of the use of eigenvectors/values -- thank you!!
Thank you so much, your explanation is simple and clear and contains alot of concepts which makes the video not boring(which math videos usually are) and intriguing
The fibonocci series example has solidified this concept in ways that I've been searching for
When I got to the part about stability and rotation I was like: “Hey Laplace Transform!”. I love the way so much of math overlaps!
Just wow! A great visual way of explaining the fundamental concept in Linear algebra. Thank you!
would.'ve really been helpful for when i was in college. profs just threw these things at us, i had no clue till this day.
Your videos are really helpfull as they graphicly and schematicly describe mathematic and physic concept that other way would be almost imposible to understand, thanks Mr. Zach for the time and effort you put on making and posting your videos on TH-cam for the public. Me and lots of other people really appreciate it.
love these videos you've made on linear alg. Im a soph ME student finishing up a course on lin alg and I've found your videos really entertaining, clarifying and well produced. Ever considered doing a video on basis vectors? properties and apps of the determinant? This is such useful math and I just wish my teachers could make these abstract topics as palatable and engaging as you have.
I feel every engineering school should show these videos to show the reason why they are learning what they are
Or maybe they could be able to inspire their students without the help of a youtuber, on account of being salaried professionals?
the best video on eingen-stuff i've ever watched! thanks a lot. i've been searching for this type of explanation for a long time
Wow, thus series of applications.. Is the best thing you are doing.. And the best thing going on the internet
These are the videos that make TH-cam great! Please continue to make this type of videos, I absolutely love them
Brilliant illustration!!! Keep up the good work Sir!
An early Christmas present. Thank you sir!!!
Very well done!! Great work. When I was learning these in linear algebra, I had no idea what they were for.
Thank you. This make the whole thing more intuitively understandable. Love your vids a lot
One of the best videos that I have found on this topic! Great work!
Great video. It was simple but technical at the same time! I loved the animations.
This is very well put together and even greater visualization than I got in Uni!
Very nice video. An extremely efficient way of visualizing and teaching math and engineering concepts. Thank you.
Thank you for this video. I've always wanted to understand what eigen stuff are ever since hearing about them in college.
Who else saw black spots on the orange dots around 11:54 (arbitrary time of course) that disappeared when you looked directly at them?
Awesome video again Zach, knowledge rich and interesting videos always
Fantastic. This plus 3B1B gives a really good understanding. This video was really awesome bro.
This was very very illuminating. You’re an excellent teacher.
I am always waiting for your videos.
I feels like 20 min of your video teaches more than my whole 8 hours of collage .
Big thanks.
💖
My brother I am from Nigeria's fall system of education so I understand . You don't just feel...you KNOW!
This was literally so beautiful!
i appreciate this video. seeing real-world applications by using abstract math is one of the most profound things i have witnessed. knowledge is the real power behind being effective in the world. thank you for educating us. it makes the world a better place. (and a less ignorant place)
First class video - very well produced and an excellent set of illustrations
How did you read my mind ?? I actually needed this video😀😀 I love this content ...this is very unique
Great video ... one of the gold nuggets of TH-cam ... first time I saw some real applications (just was number crunching to me before this). Thanks ... it is most appreciated!
Very good way of explaining eigenvalues and eigenvectors! Highly intuitive!! Thanks!
This video was awesome at teaching useful math in an interesting and accessible way! Thank you for sharing!
Brother , you are doing a great job !
Hope we get more interesting videos on some weird topics
Never seen a more intuitive video about eigen vectors than this!
I've been an engineering student in various forms for 5 years and I've studied the mechanics of calculating Eigenvectors and associated values for hour and hours. I've searched and searched for a 'simple' explanation of what an Eigenvector actually is. This is by far the best explanation I've found.
Just discovered your channel and been watching your vids, Wish I was taught like that in school ! I will teach kids in school like you do and share with them your videos from now on! Great Work! Applause from Hong Kong : )
you explained years of trying to understand linear algebra in one split second. Thank you!
Wow! I'm a machine learning engineer, and I have had studied all these concepts time and time before in the college, but I had never grasped the gist of it this good, really surprising! thanks!
Your video is pure joy for me as a math lover.
Im an engineering student( graduate level) with specialisation in control systems theory.
I've seen many explanation videos, but yours is my favourite.
If your video had been online while i took my math courses in undergraduate level, i could have saved a lot of hours :D.
You have done a great job!
This was one of the best videos I have seen explain system stability
Zach, this is a great video, just in time to my exams, now i unsderstand the perpose and how much usefull are eigenvectors and eigenvalues, colleges dont teach math in the way they should, they dont explain "why is that important?" they just give u a book. U can find motivation watching this kind of videos, congrats!
excellent explanation!.. i just understood what is eigen value and vectors.. Thank you!
I don’t know what eigenvalues and eigenvectors are essentially until I watch your great video. Thank you!
Fantastic video examples and excellent graphics.
nice video, I love the real world examples with the graphs
Woww ,you are awesome... Thanks a ton for this wonderful video . I was only knowing mathematics but was unaware of its uses ..you made me understand the subject with purpose . Thanks again to decipher this important aspect of complex mathematical world.🙏
One of the best video on understanding Eigen value problem in practical way..Thank you..
Thank you for making this video. I'm learning much here.
thank you for clearing many doubts in interesting ways..
this is a masterpiece may god bless you.
I thought I understand these topics because they are too simple I uses them a lot but now my understanding deepened
This introduction to linear dynamical systems is great. A follow-up video on chaotic systems, their phase planes and dependence on initial values will be even better, since most engineering classes don't delve into that.
good shit, it's really nice to see how you can apply things thanks a lot!
Beautifully explained and very enjoyable. I wish I could give you more than one upvote.
really loved this! put a lot of college lectures into perspective
As usual learnt a lot of stuffs!!!
Thanks for you efforts!!!really appreciate it...
YOU ARE AWESOME. WORLD REALLY NEED TEACHER LIKE YOU. YOUR INFORMATION ARE WAY MOREEEE USEFUL.
THANKYOU
Great work from Zach. Keep it up.
Dude. This video is excellent. Finally getting more intuition on why this eigenstuff is so useful. Thank you.
Glad you liked it!
This video was amazing, thank you!
This Channel has it all I need, comedy, academics, and a Star
Very nice video and very instructive !!!
Fun stuff! Another neat example is the compliance matrix in Mechanics of Materials. Here, the eigenvalues teach us something about how the elastic behaviour does its thing.
keep going, deserves 2-3 more videos on the topic.
I really like this video because now I feel like I actually understand something I rotely memorized in class. Thanks!
Man this is brilliant. I saw this video about 4 months ago. Lately been going through matrix n clustering in python and it hit me and I rushed back to this vid. Everything makes perfect sense now. Am happy it clicked 🚀
This was quite interesting. I know all the tools described herein but I hadn’t imagined how they could be put together. This linear algebra isn’t just the tools, it’s they way you think about problems that it brings out. Very nice set of examples. You’ve brought out the multiple dimensions of problem applications. Might say you’ve shown us the fields that linear algebra applies to (pun intended).
thanks for everything u do man. its just shows how simple maths can solve some of the greatest questions of humanity
This is the first video of you I watch and I am a fan now. Thanks so much for the explanation. I would like if you add example of vibrating multidegree of freedom systems as we get eigenvalues and vectors for them too as I am sure your explanation will add too much.
Although I don’t fully understand, I’ve been amazed! Such a brilliant video! Thank you very much!
Fantastic explanation. Many thanks
WOW !
Many ideas just pop in my brain , while seeing this video ... incredible!
Very detailed and thought provoking content.
Your videos are a gift to humanity.
Thanks a ton for such a wonderful video! Simply amazing... Namaste!