How to rotate in higher dimensions? Complex dimensions? | Lie groups, algebras, brackets #2

Part 3:    • What is Lie theory? Here is the big pictur...   Around 11:50, can't imagine that this error got in - it should have been SU(n) = {U in U(n), det U = 1}. Orthogonal and unitary groups. Rotational symmetries, real and complex, are particularly useful in the field of Lie theory, because their (complexified) Lie algebras, together with that of the symplectic group Sp(n), are the only infinite families of simple Lie algebras. This video is to familiarise with the SO(n), SU(n) notations, and provides further motivation to study Lie theory. Files for download: Go to https://www.mathemaniac.co.uk/download and enter the following password: orthogonalunitary Video chapters: 00:00 Introduction 01:04 Real rotation in n dimensions 07:03 Complex rotation Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels: https://forms.gle/QJ29hocF9uQAyZyH6 If you want to know more interesting Mathematics, stay tuned for the next video! SUBSCRIBE and see you in the next video! If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I use PowerPoint, GeoGebra, and (sometimes) Mathematica to produce the videos. Social media: Facebook:   / mathemaniacyt   Instagram:   / _mathemaniac_   Twitter:   / mathemaniacyt   Patreon:   / mathemaniac   (support if you want to and can afford to!) Merch: https://mathemaniac.myspreadshop.co.uk Ko-fi: https://ko-fi.com/mathemaniac [for one-time support] For my contact email, check my About page on a PC. See you next time!