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- Fundamental group of the special orthogonal group SO(n)
You can use the exact sequence of homotopy groups you mention (without knowing the maps) to get the result once you know $\pi_1(SO(3))$
- Dimension of SO (n) and its generators - Mathematics Stack Exchange
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- 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 mention Tue; if he has a son daughter both born on Tue he will mention the son, etc
- lie groups - Lie Algebra of SO(n) - Mathematics Stack Exchange
$\begingroup$ Well, to answer your question, you should show that $\mathfrak{so}(n)$ consists of skew-symmetric matrices (I am sweeping something under the rug here, because you need to lower one index of an element of $\mathfrak{so}(n)$ in order to get a skew-symmetric matrix with two indices down)
- Homotopy groups O(N) and SO(N): $\\pi_m(O(N))$ v. s. $\\pi_m(SO(N))$
I have known the data of $\\pi_m(SO(N))$ from this Table: $$\\overset{\\displaystyle\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\quad\\textbf{Homotopy groups of
- Improper integral of sin(x) x from zero to infinity
I was having trouble with the following integral: $\int_{0}^\infty \frac{\sin(x)}{x}dx$ My question is, how does one go about evaluating this, since its existence seems fairly intuitive, while its
- What does versus mean in the context of a graph?
$\begingroup$ I can honestly say i don't think i have heard the "versus" terminology used in math courses, but i hear it and see it used all the time in other sciences courses, chemistry, physics, etc Ive wondered about it for so long but am finally stuck on something, where the interpretation is makes or breaks the answer
- Prove that the manifold $SO(n)$ is connected
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