Group Theory Lecture 1.3 Examples: The Orthogonal Group of the Plane

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00:00 Recap
00:44 Problems
00:48 Rotations of R^2
03:00 Reflections in R^2
06:20 How Reflections and Rotations Interact
10:20 Compositions of Two Reflections
12:24 Group of Orthogonal Transformations
19:50 Characterization of the Orthogonal Group of the Plane

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Комментарии
Автор

Bhaiya thanks for all your videos and please keep continue to put videos of undergraduate and even of graduate because rigorous maths is very interesting where we define or assume some statement and derive beautiful things Thanks a lot

AIbeast
Автор

Couldn't all reflections be represented as just rotations? If so, what separates SO2(R) from O2(R)? Not to mention, if O2(R) contains both reflections and rotations and is also a group, wouldn't that break the rule of the uniqueness of the identity considering that T0(v) is equivalent to Sv(v)? I do understand that the transformation taking place is unique but in that case why make the distinction between reflections and rotations?

existential_turtle
Автор

Bhaiya can you suggest me some formal set theory and mathematical logic material because I think that with both the help of these as foundation of maths we can describe everything rigorously and not thing will remain vague or undefined

AIbeast