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Welcome to the language barrier between physicists and mathematicians It's fairly informal and talks about paths in a very Physicists prefer to use hermitian operators, while mathematicians are not biased towards hermitian operators

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What is the fundamental group of the special orthogonal group $so (n)$, $n>2$ 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 The answer usually given is

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I have known the data of $\\pi_m(so(n))$ from this table The generators of $so(n)$ are pure imaginary antisymmetric $n \\times n$ matrices Yes but $\mathbb r^ {n^2}$ is connected so the only clopen subsets are $\mathbb r^ {n^2}$ and $\emptyset$ In case this is the correct solution

Why does the probability change when the father specifies the birthday of a son 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. U(n) and so(n) are quite important groups in physics