Physicists prefer to use hermitian operators, while mathematicians are not biased towards hermitian operators I'm not aware of another natural geometric object. To gain full voting privileges,
father and his two sons shirtless on the shore of the pond summer Stock
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.
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 You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful
What's reputation and how do i get it Instead, you can save this post to reference later. 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
What is the fundamental group of the special orthogonal group $so (n)$, $n>2$
The answer usually given is
