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Welcome to the language barrier between physicists and mathematicians It is clear that (in case he has a son) his son is born on some day of the week. 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 $so (n)$, $n>2$ A lot of answers/posts stated that the statement does matter) what i mean is 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) s o (n) are pure imaginary antisymmetric n×n n × n matrices How can this fact be used to show that the dimension of so(n) s o (n) is n(n−1) 2 n (n 1) 2 I know that an antisymmetric matrix has n(n−1) 2 n (n 1) 2 degrees of freedom, but i can't take this idea any further in the demonstration of the proof

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I have a potentially simple question here, about the tangent space of the lie group so (n), the group of orthogonal $n\times n$ real matrices (i'm sure this can be.

U (n) and so (n) are quite important groups in physics I thought i would find this with an easy google search What is the lie algebra and lie bracket of the two groups? In case this is the correct solution

Why does the probability change when the father specifies the birthday of a son