This is Lie groups, manifolds and etc. stuff, and if you haven't yet studied this it may look like chinese to you: the tangent space of U(n) at the unit element is just the space of all anti-hermitian matrices.

You may try to read the following:

http://math.ipm.ac.ir/shahshahani/diff/chapter1.pdf

What you want is at the beginning of page 13, but you need a rather decent load of background in higher maths to udnerstand it.

Tonio