Lie Groups #2 - The orthogonal group SO(2)

Рет қаралды 10,309

Күн бұрын

This video will introduce the orthogonal groups, with the simplest example of SO(2). I will discuss how the group manifold should be realised as topologically equivalent to the circle S^1, to start building intuition about the geometric significance of Lie groups (as manifolds).
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Пікірлер: 23

@Sara-vm2sz 3 жыл бұрын

How is it possible that I couldn't understand this after a semester of lectures + typed lecturer's notes, but it took only two of your videos to clear everything up lol You're doing such a great job at explaining all these super complex topics!

@kikihope 3 жыл бұрын

thank you!! you cleared up some concepts that were making me a bit confused !! and btw this video made me so happy 💗 your dog looks stunning

@Jinsun202 3 жыл бұрын

Man, you cleared up so many things for me, cheers! Chocolate lab is awesome too!!

@matthewharrison8531 2 жыл бұрын

I love your style of teaching. Thank you

@AMADEOSAM 6 ай бұрын

Great explanation! Thanks

@darashayda1 2 жыл бұрын

Excellent and accurate presentation.

@pugazharasuad 3 жыл бұрын

If possible, in a future video talk a bit about the link between SO(2) and U(1) and SO(3) and SU(2) please?

@alijoueizadeh2896 2 жыл бұрын

Thank you!

@aleksander5127 3 ай бұрын

Obrigado!

@th5k189 2 жыл бұрын

Hello. Idk if you will see it considering you haven't uploaded for a long time. But I was asked to give geometric interpretation of SO(2) and was able to prove that SO(n)= intersection of O(n) and SLn(R). I tried my best to understand what you said(but we still didn't take this in class and I'm trying my best to finish asst as fast as I can). Can you please help me?

@michaelaristidou2605 Жыл бұрын

The matrix representation you wrote is not for O(2), but for SO(2). I e. the rotations. The group O(2) contains also the reflection matrices.

@kronikevaporation6007 2 жыл бұрын

What is the purpose of trying to realize group theory in geometric fashion? I am from physics background, and I can't seem to think any.

@jspa711 Жыл бұрын

I think this is caused by outer rotation being a special orthogonal rotation , or the axes don’t change while the inner rotation of the revolving coin being just a simple orthogonal rotation, or the axes are being flipped. This, the outer rotation only allows for a determinate of 1 while the inner rotation allows the determinate to be -1 or +1 which would mean that the latter has two eigen states for every one of the former. The inner rotation, allowing for the negative determinate completes a full real rotation around its own axis with a negative orientation to the fixed axis while the outer rotation still has not achieved a full rotation with a positive orientation. Bachelors of physics here, so I may not be articulating the math correctly. Please someone confirm or correct me.

@kevinsalipante5013 Жыл бұрын

Clicked for the dog, stayed for the math

@domc3743 3 жыл бұрын

can you do Q and A please?

@WHYBmaths 3 жыл бұрын

I'll do my best to answer any questions in the comments!

@domc3743 3 жыл бұрын

@@WHYBmaths okay, what university did you go to, and how old are you? i am only asking because you seem quite young and intelligent, have a nice day.

@WHYBmaths 3 жыл бұрын

I'm 23, just finished a masters in mathematical physics at the University of Nottingham! It was my dream to do a PhD and eventually become an academic to study quantum gravity, but having seen how bleak the prospects are and how competitive the research environment can be I decided it wouldn't be a sensible option given I already struggle with mental health. I'm just going to keep myself sane by continuing to make these videos and doing research on my own time!

@farhanrafid8584 3 жыл бұрын

@@WHYBmaths Do your mental health problems belong to this set? {OCD, depression, anxiety, Bipolar Disorder, n-polar disorder, ADHD, hormonal imbalance, hopelessness}?

@farhanrafid8584 3 жыл бұрын

@@WHYBmaths If you want, I can chat with you about mental health and help you, I myself suffered a lot and I have been cured after 3 years, therapy still going on. I thought if I tell you what my therapist told me, it would be nice.