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I have known the data of $\\pi_m(so(n))$ from this table Instead, you can save this post to reference later. To gain full voting privileges,

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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

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 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. Welcome to the language barrier between physicists and mathematicians Physicists prefer to use hermitian operators, while mathematicians are not biased towards hermitian operators

I'm not aware of another natural geometric object.

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. 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

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