Dimension of SO (n) and its generators - Mathematics Stack …
Nov 18, 2015 · The generators of SO(n) S O (n) are pure imaginary antisymmetric n × n n × n matrices. How can this fact be used to show that the dimension of SO(n) S O (n) is n(n−1) 2 n …
Universal covering group and fundamental group of $SO(n)$
If H H is a topological group which is both path-connected and locally path-connected (i.e. a connected Lie group such as SO(n) S O (n)), then any path-connected cover of H H inherits a …
geometry - Find the coordinates of a point on a circle
I have a circle like so Given a rotation θ and a radius r, how do I find the coordinate (x,y)? Keep in mind, this rotation could be anywhere between 0 and 360 degrees. For example, I have a radiu...
lie groups - Lie Algebra of SO (n) - Mathematics Stack Exchange
Apr 24, 2017 · Welcome to the language barrier between physicists and mathematicians. Physicists prefer to use hermitian operators, while mathematicians are not biased towards …
Fundamental group of the special orthogonal group SO(n)
Question: What is the fundamental group of the special orthogonal group , n> 2? Clarification: The answer usually given is: Z2. But I would like to see a proof of that and an isomorphism …
Boy Born on a Tuesday - is it just a language trick?
The only way to get the 13/27 answer is to make the unjustified unreasonable assumption that Dave is boy-centric & Tuesday-centric: if he has two sons born on Tue and Sun he will …
The Tuesday Birthday Problem - Mathematics Stack Exchange
In case this is the correct solution: Why does the probability change when the father specifies the birthday of a son? (does it actually change? A lot of answers/posts stated that the statement …
Homotopy groups O(N) and SO(N): $\\pi_m(O(N))$ v.s.
Oct 3, 2017 · I have known the data of $\\pi_m(SO(N))$ from this Table: $$\\overset{\\displaystyle\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\quad\\textbf{Homotopy …
What does "versus" mean in the context of a graph?
I would agree with the rule " [dependent] versus [independent]." The word "versus" can mean "compared with," and it more frequently makes sense to compare a dependent value with its …
Why do three non collinears points define a plane?
Intuitively it's because the dimension of a plane is 2 so you need exactly two linearly independent vectors to generate a plane. The three points are the origin and the tips of the two vectors, you …