The applications of eigenvectors and eigenvalues | That thing you heard in Endgame has other uses

This video covers the applications of eigenvectors and eigenvalues (in and outside of mathematics) that I definitely didn't learn in school.

►My Setup:

[johnathancorgan]

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.

[shama_k]

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

[yummyzerg]

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.

[jacob-magnuson]

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!

[KeepingUp_withAI]

Aww yes ! That feeling when you just finished your masters in computer science and everything on this video made perfect sense.

[xicufwm]

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!

[RM-zxee]

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!

[sukalyanroy]

Love your videos Bro.. in an age where school is killing interest in the sciences, your videos keep my curiosity and interest alive... ❤️❤️

[johnhutchinson]

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.

[boggless]

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

[Matttincho]

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.

[NickDolgy]

This is great! Thank you! Glad to be your Patreon supporter and to be able to see your videos first!

[matteovaiente]

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.

[MistaWu]

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...

[gyudon]

watching this now after just finishing my bachelors in mechanical engineering and going onwards to a masters in computational engineering. feels like the most amazing application-based review video. THUMBS UP!

[diyoswidhi]

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

[philblandford]

I understood the geometric interpretation of eigenvalues/vectors pretty well, and had a working knowledge of the applications in DEs and things like PCA, but without a real intuition for why it worked - this is the first video I've seen that really connected them for me, thanks.

[BudgiePanic]

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

[icntthinkofanam]

The fibonocci series example has solidified this concept in ways that I've been searching for

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! 👍