Quaternions EXPLAINED Briefly

This is a video I have been wanting to make for some time, in which I discuss what the quaternions are, as mathematical objects, and how we do calculations with them. In particular, we will see how the fundamental equation of the quaternions i^2=j^2=k^2=ijk=-1 easily generates the rule for quaternion multiplication. For the sake of brevity, I don't cover the famous application to 3D rotations in this video (perhaps in a subsequent one) but, of course, one must first know how to multiply two quaternions before talking about specific applications.

[klt]

I haven't finished watching the video yet, but I came down to thank you for using black background and white text. EVERYONE SHOULD DO LECTURES THIS WAY!!! My eyes are not burning for once holy shit dude.. THANK YOU

[peternolan]

Hello,

Many thanks indeed for uploading this set of five videos about quaternions. Most interesting. I'm 63 and now at last I know about quaternions that were discovered by Hamilton an Irish mathematician as you know. I live not too far away from the place a canal where the plaque with his formulation of quaternions is written at the spot where it all became clear to Hamilton while he was walking on his way to his university Trinity College Dublin from where he lived that was what is Dunsink Observatory today and then.

All the best,

Peter Nolan.(Ph.D., experimental physics). Dublin. Ireland.

[wisdomokafor]

Thanks so much you really saved me. I could not find anyone who could explain this topic better than this

[antoinedevldn]

This is how beautiful a concept can be explained! Flawless, thanks a lot :)

[benjaminv]

I still learn very (relatively speaking) math, in fact I have only briefly touched complex numbers and i, yet this video was very intresting and taught me some basic quaterion rules. Now I probably won't use this knowledge for another few semesters but videos like these always keep me motivated to learn more and get there!

[SuperAcousticDude]

This was wonderfully explained. I cant tell you how many channels ive been thru trying to find something like this.
Many try to flex their knowledge of the topic without realising that some of their viewers are there to learn the topic from the ground up.
Amazing work!

[nodoesart]

I have a presentation to do in my first year of university (i'm doing a double degree in maths and physics) and we chose quaternions with my two friends. I'm the only one who speaks English so I'll be able to brag and make them think I'm a quaternion expert because I watched your video. It was really well-explained and easy to understand, thank you !

[PARISAROMAN]

No angry comments, the opposite, I am happy to see and listen your awesome exposition. Thank you very much Mathoma.

[tombruckner]

That's the first time I actually understood what Quaternions are all about. Kudos to you!

[VladTepesh]

I find the quaternion multiplication table very informative, as well as a refresher from the other parts of your video. Thanks!

[hkxlolz]

at 1:31 when you explain so simply the R^2, you have my like on the video

[nexusclarum]

I like how you write the letter 'q'. Also good explanation.

[efraingbj]

Thanks for the video, I'm currently working on a robotics project and it's the first time I heard about quaternions, your explanation was pretty spot-on as an introduction to the topic! Also your channel seems really interesting, great job! Greetings from the other side of the wall!

[rohan.fernando]

A brilliant explanation of quaternion algebra. William Rowan Hamilton would surely be impressed. Well done.

[OomptzMusic]

Love the "blackboard" presentation. Great video 👍

[lukastheinfinite]

You think and explain in the way I do it. Kudos sir! And thank you for your effort!

[xfry]

OMG OMG OMG!! I was stuck reading this topic in a book and you finally has given to me the final understanding about this topic! You are amazing dude

[redrevelations]

Thank you very much for explaining quaternions in a very simple way. It helped me a lot.

[rlenclub]

I thought that *brief* was the wrong word to use here until I remembered you're explaining quaternions.

[craigruchman]

My math only goes up to abstract algebra, so this was a nice intro for me, thanks