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 …
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 …
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 …
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 …
Probability that two non-twin siblings are born on same day
Aug 25, 2020 · 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 …
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 …
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 …
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 …
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, …
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.