Google and eigenvalues

Google and eigenvalues. We describe the Pagerank algorithm, which was one of the algorithms used by Google for their search engine. For this, we rank the websites using an importance vector vector and write the system as a Markov chain, using matrices. Then we diagonalize the matrix using linear algebra, more precisely eigenvalues and eigenvectors. Finally, by taking limits of the matrix, we can determine which website reigns supreme. This probably has applications in data science and neural networks as well.

[lizziethelemon]

Dr Peyam! I have my Linear Algebra exam this week! You've helped me revise a lot and understand many of the concepts! I'm so grateful for you and grateful you exist. You're a wonderful person and such an empathetic teacher! 💛

[hungryplate]

Learning about this in my data science classes. Truly exciting stuff!

[mastershooter]

"80% of mathematics is linear algebra"

-Raoul Bott

[HelloWorld-dqpn]

Classic Markov chain problem!! For those who dont understand why 1 is always an eigenvalue of a Markov Matrix, consider Av=cv for some constant c and some markov vector v(and of course, the markov matrix A), take A to be a 2x2 matrix, for simplicity. Now multiply both sides by the row vector k= [1 1], so kAv =ckv, which gives c=1.

[bagusamartya]

I remember encountering your videos back in high school and understood only like 2% of it. I still don't understand lots, but I'm glad to know that you're still going strong educating people through internet

[Ryokusei]

I have two questions...

1. What assures us that the others elements of D are less than 1?

2. What is the name of the theorem mentioned in 10:04?

Pd: great video :)

[falconajc]

this is awesome, I just finished linear algebra 1, and seeing how concepts like eigenvalues interact in the real world is super cool

[titian]

Abstractions are so cool! How they translate to real world ideas is even cooler!

[wryltxw]

what a joy to see math so clearly explained. that was awesome! you basically capture the essence of it really well.

[DrWeselcouch]

Good timing! I just gave my students a project on this topic!

[colleen]

We actually learned about this the last day of my linear algebra class! (Last year)

[garyhuntress]

I really like the linear algebra problems

[shamaldesilva]

This is amazing !!!! . Please make more videos like this where you are explaining how these technologies are using Mathematics 🤩🤩🤩🤩🤩🤩

[gatitoconsueter]

great video, all your videos in fact. It's good to see someone explaining in an easy way how this works, I've been following you on yt for years and you keep all the quality and motivation, keep it up. There is a book called Google's PageRank and Beyond: The Science of Search Engine Ranking. I read it a while back and the book discussed some methods to find eigenvalues ​​faster and optimize algorithms etc. Sometimes we don't appreciate that, but it is important to study and develop it because it is our daily tool to work, at least in modern society. Un abrazo Doc y gracias por el video...;0

[tristanmoller]

Love to see the math I learned applied! I study mech engineering not computer science but we also have some lin algebra.

But in mech engineering, it feels like the only reason to study linear algebra for 2 semesters is to solve differential equation systems (except for statistics maybe).
So seeing linear algebra being useful by itself is pretty cool!

[Enigma]

I've seen a similar analysis applied to the game of Monopoly. There was an article about that years ago in Scientific American.

[holyshit]

5:30, and that's how power method works for dominant eigenvalue and corresponding eigenvector

[lebesgue-integral]

You are the happiest mathematician of youtube!
This is awesome

[vivvpprof]

This is really cool but not having used algebra in a few years I can just barely remember "yeah, eigenproblem, we did that" but the details are murky. I didn't even remember matrix multiplication is associative :D I thought you have to do this from right to left

[uraniumra]

Cool system, and even cooler video! As a physics student, as soon as you said transition matrix, I got flashbacks of hopping probabilities from quantum classes D: (also, go bears!!)