I am not sure how to find the dimension of U(n).
Suggestions i have been given are: ((n^2) - n)) / 2
But i don't know which (if either) of these is correct, and how they are found.
Thanks for any help
To get the tangent space at , differentiate at the equation defining implicitly the manifold (here, ) : it is the space of matrices such that . If , this reduces to . (More formally, the tangent space at A is the kernel of the differential at A of a (submersive?) map such that the manifold is a level set of (at least locally at ))