lie groups - Lie Algebra of SO (n) - Mathematics Stack Exchange
Apr 24, 2017 · Welcome to the language barrier between physicists and mathematicians. Physicists prefer to use hermitian operators, while mathematicians are not biased towards …
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: $\mathbb {Z}_2$. But I would like ...
Prove that the manifold $SO (n)$ is connected
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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 …
Dimension of SO (n) and its generators - Mathematics Stack …
Nov 18, 2015 · The generators of $SO(n)$ are pure imaginary antisymmetric $n \\times n$ matrices. How can this fact be used to show that the dimension of $SO(n)$ is $\\frac{n(n-1 ...
general topology - The special orthogonal group is a manifold ...
Jun 28, 2014 · yes but $\mathbb R^ {n^2}$ is connected so the only clopen subsets are $\mathbb R^ {n^2}$ and $\emptyset$
Q. 18 from A first course in probability by Sheldon Ross
Apr 12, 2024 · Each of 20 families selected to take part in a treasure hunt consist of a mother, father, son, and daughter. Assuming that they look for the treasure in pairs that are randomly …
The Tuesday Birthday Problem - Mathematics Stack Exchange
In case this is the correct solution: Why does the probability change when the father specifies the birthday of a son? (does it actually change? A lot of answers/posts stated that the statement …
Are $SO(n)\\times Z_2$ and $O(n)$ isomorphic as topological …
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If a couple has 3 girls, what is the probability that their 4th child ...
Jan 22, 2017 · What is the probability that their 4th child is a son? (2 answers) Closed 8 years ago. As a child is boy or girl; this doesn't depend on it's elder siblings. So the answer must be …