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Welcome to the language barrier between physicists and mathematicians To gain full voting privileges, Physicists prefer to use hermitian operators, while mathematicians are not biased towards hermitian operators
What is the fundamental group of the special orthogonal group $so (n)$, $n>2$ Yes but $\mathbb r^ {n^2}$ is connected so the only clopen subsets are $\mathbb r^ {n^2}$ and $\emptyset$ The answer usually given is
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 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.
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 It's fairly informal and talks about paths in a very 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. If he has two sons born on tue and sun he will mention tue If he has a son & daughter both born on tue he will mention the son, etc.
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