What is an Eigenvector?

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:

Or after the fact on:

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):

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:

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:

[lradmclovin]

You just ended years of confusion in 4 minutes. Thank you

[yongyoon]

Embarrassingly, I admit that finally I got some meaning in eigenvector and eigenvalue after all those years. Thanks for the insight.

[Louise]

i'm a third year physics major and this was the best explanation i've ever seen, by far. good job!

[jessfairbairn]

You're the first person to have successfully explained eigenvectors in a way I can visualise, so thank you!

[LarryPanozzo]

If only university professors knew how to explain this intuitively and used animations like this.

[wrcz]

I literally got chills over my spine from finally understanding. And it is so bloody simple! Thank you! Absolutely brilliant

[priyankaverma]

Wonderful explanation. The geometrical meaning of eigen vector is explained very well.
ThankYou for such a nice explaination

[prabhusingh]

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.

[melontusk]

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.

[MatTags]

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.

[ravinishachincholkar]

Thank you 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!!!!

[CrystalStarlight]

A definition was exactly what I needed! I'm in linear algebra and this helps understand a bit of what's happening.

[insideabrain]

This channel is pure gold. thank you for sharing your understanding with us!

[albertbatfinder]

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.

[adminassistant]

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?

[whomisac]

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.

[drmcstr]

one of the best quick explanation of eigenvectors/eigenvalues yet!

[curiash]

One of the best video on intuitive explanation of eigenvector.

[snokful]

Examiner (no live lectures any more) linked to this at start of course. Very helpful beginning. Thankyou. Gave me an appetite to understand more.

[KingFredrickVI]

Finally! You haven't uploaded in forever!

This is a really nice video man :D good job. Explained it pretty well I think.