Age problem of father and son - Mathematics Stack Exchange
A father's age is now five times that of his first born son. Six year from now, the old man's age will be only three times that his first born son. Find age of each.
Homotopy groups O(N) and SO(N): $\\pi_m(O(N))$ v.s. $\\pi_m(SO(N))$
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 …
Why $\\operatorname{Spin}(n)$ is the double cover of $SO(n)$?
Dec 16, 2024 · You can let $\text {Spin} (n)$ act on $\mathbb {S}^ {n-1}$ through $\text {SO} (n)$. Since $\text {Spin} (n-1)\subset\text {Spin} (n)$ maps to $\text {SO} (n-1)\subset\text {SO} (n)$, you could …
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 hermitian operators. …
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
The question really is that simple: Prove that the manifold $SO (n) \subset GL (n, \mathbb {R})$ is connected. it is very easy to see that the elements of $SO (n ...
Explicit Lie group embedding of $O (n)$ into $SO (n+1)$
May 25, 2023 · oh and if you’re following Lee’s book, then he definitely mentions somewhere that Lie group homomorphisms have constant rank, which is why it suffices to consider things at the identity. …
Showing SO(n) is a compact topological group for every n
May 18, 2023 · You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation and how do I …
What is the relationship between SL (n) and SO (n)?
I'm in Linear Algebra right now and we're mostly just working with vector spaces, but they're introducing us to the basic concepts of fields and groups in preparation taking for Abstract Algebra la...
How to find the difference between the son's and mother's age if it ...
Oct 23, 2019 · A son had recently visited his mom and found out that the two digits that form his age (eg :24) when reversed form his mother's age (eg: 42). Later he goes back to his place and finds out that …