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  1. 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 $\pi_1(SO(3))$.

  2. Dimension of SO (n) and its generators - Mathematics Stack …

    Nov 18, 2015 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …

  3. 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 …

  4. lie groups - Lie Algebra of SO(n) - Mathematics Stack Exchange

    Apr 24, 2017 · $\begingroup$ Well, to answer your question, you should show that $\mathfrak{so}(n)$ consists of skew-symmetric matrices (I am sweeping something under the …

  5. In a family with two children, what are the chances, if one of the ...

    May 27, 2016 · For example, suppose there is a social science study on 2 child families with at least 1 daughter-- in this situation, about 1/3 of the families will be daughter-daughter, 1/3 will …

  6. Prove that the manifold $SO(n)$ is connected

    Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …

  7. Improper integral of sin(x)/x from zero to infinity

    Jun 14, 2017 · 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 …

  8. orthogonality - What does it mean when two functions are …

    Jul 12, 2015 · Vectors are orthogonal not if they have a $90$ degree angle between them; this is just a special case. Actual orthogonality is defined with respect to an inner product.

  9. 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 …

  10. 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, …

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