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Welcome to the language barrier between physicists and mathematicians I'm not aware of another natural geometric object. 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 $so (n)$, $n>2$ What is the lie algebra and lie bracket of the two groups? 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 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 chosen from the 80

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 I thought i would find this with an easy google search