Hi, I'm having trouble starting out with this question:
"What is/Define the tangent space of U(n) at the identity matrix?"
If anyone could give me a hint at how to start working this out I'd be most appreciative.
Hi, I'm having trouble starting out with this question:
"What is/Define the tangent space of U(n) at the identity matrix?"
If anyone could give me a hint at how to start working this out I'd be most appreciative.
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