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Welcome to the language barrier between physicists and mathematicians Instead, you can save this post to reference later. 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's reputation and how do i get it The answer usually given is

I have known the data of $\\pi_m(so(n))$ from this table

The question really is that simple Prove that the manifold $so(n) \\subset gl(n, \\mathbb{r})$ is connected It is very easy to see that the elements of $so(n)$ are. The generators of $so(n)$ are pure imaginary antisymmetric $n \\times n$ matrices

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? I'm not aware of another natural geometric object.

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.

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