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Fundamental group of the special orthogonal group SO(n)
Question: What is the fundamental group of the special orthogonal group SO(n), n> 2? Clarification: The answer usually given is: Z2. But I would like to see a proof of that and an …
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 …
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 …
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 …
lie groups - Lie Algebra of SO (n) - Mathematics Stack Exchange
Apr 24, 2017 · Where a, b, c, d ∈ 1, …, n a, b, c, d ∈ 1, …, n. And so(n) s o (n) is the Lie algebra of SO (n). I'm unsure if it suffices to show that the generators of the ...
Improper integral of sin(x)/x from zero to infinity
Jun 14, 2017 · I was having trouble with the following integral: ∫∞0 sin (x) x dx. My question is, how does one go about evaluating this, since its existence seems fairly intuitive, while its solution, …
Prove that the manifold $SO(n)$ is connected
The question really is that simple: Prove that the manifold SO(n) ⊂ GL(n, R) is connected. it is very easy to see that the elements of SO(n) are in one-to-one correspondence with the set of …
Lie Algebra of U(N) and SO(N) - Mathematics Stack Exchange
Oct 8, 2012 · U(N) and SO(N) are quite important groups in physics. I thought I would find this with an easy google search. Apparently NOT! What is the Lie algebra and Lie bracket of the …
orthogonality - What does it mean when two functions are …
Jul 12, 2015 · The concept of orthogonality with regards to functions is like a more general way of talking about orthogonality with regards to vectors. Orthogonal vectors are geometrically …
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