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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)
- geometry - Find the coordinates of a point on a circle - Mathematics . . .
The standard circle is drawn with the 0 degree starting point at the intersection of the circle and the x-axis with a positive angle going in the counter-clockwise direction
- Probability that two non-twin siblings are born on same day
The simplest model assumes that there are 365 days in a year, each sibling having the same probability of 1 365 of being born on any of those days, and their births are independent
- 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 orthogonal groups
- 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
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