Son daughter caught naked together. Jun 28, 2014 · yes but $\mathbb R^ {n^2}$ is connected so the only clopen subsets are $\mathbb R^ {n^2}$ and $\emptyset$ I have been wanting to learn about linear algebra (specifically about vector spaces) for a long time, but I am not sure what book to buy, any suggestions? Oct 8, 2012 · U(N) and SO(N) are quite important groups in physics. Apparently NOT! What is the Lie algebra and Lie bracket of the two groups?. Apparently NOT! What is the Lie algebra and Lie bracket of the two groups? Dec 16, 2024 · You can let $\text {Spin} (n)$ act on $\mathbb {S}^ {n-1}$ through $\text {SO} (n)$. It's fairly informal and talks about paths in a very 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 does matter) What I mean is: It is clear that (in case he has a son) his son is born on some day of the week. I'm not aware of another natural geometric object 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 does matter) What I mean is: It is clear that (in case he has a son) his son is born on some day of the week. Upvoting indicates when questions and answers are useful. I thought I would find this with an easy google search. How can this fact be used to show that the dimension of $SO(n)$ is $\\frac{n(n-1 Jun 28, 2014 · yes but $\mathbb R^ {n^2}$ is connected so the only clopen subsets are $\mathbb R^ {n^2}$ and $\emptyset$ Oct 8, 2012 · U(N) and SO(N) are quite important groups in physics. Apparently NOT! What is the Lie algebra and Lie bracket of the two groups? Apr 24, 2017 · Welcome to the language barrier between physicists and mathematicians. Since $\text {Spin} (n-1)\subset\text {Spin} (n)$ maps to $\text {SO} (n-1)\subset\text {SO} (n)$, you could then use the argument directly for $\text {Spin} (n)$, using that $\text {Spin} (3)$ is simply connected because $\text {Spin} (3)\cong\mathbb {S}^3$. Physicists prefer to use hermitian operators, while mathematicians are not biased towards hermitian operators. But I would like Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges, Oct 3, 2017 · I have known the data of $\\pi_m(SO(N))$ from this Table: $$\\overset{\\displaystyle\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\quad\\textbf{Homotopy groups of Nov 18, 2015 · The generators of $SO(n)$ are pure imaginary antisymmetric $n \\times n$ matrices. Apr 24, 2017 · Welcome to the language barrier between physicists and mathematicians. How can this fact be used to show that the dimension of $SO(n)$ is $\\frac{n(n-1 The question really is that simple: Prove that the manifold $SO(n) \\subset GL(n, \\mathbb{R})$ is connected. Apr 24, 2017 · Welcome to the language barrier between physicists and mathematicians. What's reputation and how do I get it? Instead, you can save this post to reference later. But I would like Nov 18, 2015 · The generators of $SO(n)$ are pure imaginary antisymmetric $n \\times n$ matrices. Oct 19, 2019 · You'll need to complete a few actions and gain 15 reputation points before being able to upvote. it is very easy to see that the elements of $SO(n)$ are Oct 3, 2017 · I have known the data of $\\pi_m(SO(N))$ from this Table: $$\\overset{\\displaystyle\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\quad\\textbf{Homotopy groups of I've found lots of different proofs that SO(n) is path connected, but I'm trying to understand one I found on Stillwell's book "Naive Lie Theory". So for instance, while for mathematicians, the Lie algebra $\mathfrak {so} (n)$ consists of skew-adjoint matrices (with respect to the Euclidean inner product on $\mathbb {R}^n$), physicists prefer to multiply them Question: What is the fundamental group of the special orthogonal group $SO (n)$, $n>2$? Clarification: The answer usually given is: $\mathbb {Z}_2$. bkn86om rbzi f7qvho emn zrjkwv hlsl8 xrr nwbbg dc6bld c1vvsu