Dimension of Lorentz group

Question

Consider the Lorentz group $SO(1, n)$. I would be interested in knowing the dimension of this Lie group for general $n$. Can you tell me, what its dimension is? Thank you in advance!

Answer 1

The dimension of the orthogonal group with any signature over an $n$ dim space is $n$ choose 2. This is because every rotation is determined by a plane and an angle, it takes two independent vectors out of $n$ independent vectors in your space to determine a plane. So $ \text{SO}(n)$, $\text{SO}(1,n-1) $, and $ \text{SO}(n-1,1) $ all have dimension $ {n\choose 2 } = \frac{n(n-1)}{2} $