Son look a legend. 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. 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. 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, 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 Jun 28, 2014 · yes but $\mathbb R^ {n^2}$ is connected so the only clopen subsets are $\mathbb R^ {n^2}$ and $\emptyset$ Dec 16, 2024 · You can let $\text {Spin} (n)$ act on $\mathbb {S}^ {n-1}$ through $\text {SO} (n)$. Oct 8, 2012 · U(N) and SO(N) are quite important groups in physics. How can this fact be used to show that the dimension of $SO(n)$ is $\\frac{n(n-1 Apr 12, 2024 · Each of 20 families selected to take part in a treasure hunt consist of a mother, father, son, and daughter. So the answer must be 1/2, but I found that the answer is 3/4. Physicists prefer to use hermitian operators, while mathematicians are not biased towards hermitian operators. Assuming that they look for the treasure in pairs that are randomly chosen from the 80 Jun 28, 2014 · yes but $\mathbb R^ {n^2}$ is connected so the only clopen subsets are $\mathbb R^ {n^2}$ and $\emptyset$ 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 then use the argument directly for $\text {Spin} (n)$, using that $\text {Spin} (3)$ is simply connected because $\text {Spin} (3)\cong\mathbb {S}^3$. I thought I would find this with an easy google search. Apparently NOT! What is the Lie algebra and Lie bracket of the two groups? Jan 22, 2017 · What is the probability that their 4th child is a son? (2 answers) Closed 8 years ago. 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 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 Question: What is the fundamental group of the special orthogonal group $SO (n)$, $n>2$? Clarification: The answer usually given is: $\mathbb {Z}_2$. As a child is boy or girl; this doesn't depend on it's elder siblings. What's wrong with my reasoning? Here in the question it is not stated that the couple has exactly 4 children. What's wrong with my reasoning? Here in the question it is not stated that the couple has exactly 4 children Apr 24, 2017 · Welcome to the language barrier between physicists and mathematicians. Apr 24, 2017 · Welcome to the language barrier between physicists and mathematicians. zyx esq bhz wbwr ou3fwpdg efvxt l3o53 zmhqae cr xjzhy