Lie groups

[meteor]

Ok, is my blame for not wanting to buy a Group theory book, but anyway:
I'm searching the correct definition for the Lie groups SO(n) and SU(n), and these are the definitions that I've found until now:

SO(n): -Is the Lie group of n*n real orthogonal matrices with
determinant equal to one
-Is the Lie group of n*n special real orthogonal matrices
-Is the Lie group of n*n orthogonal matrices with
determinant equal to one

SU(n): -Is the Lie group of special complex unitary n*n matrices
-Is the Lie group of n*n unitary matrices with determinant
equal to one

Well, what's the correct definition?? Or, if they are wrong, what's the exact definition of SO(n) and SU(n)?

Thanks

[mathman]

I'm a little rusty on the definitions, but here goes. Special means determinant = 1. Orthogonal matrices are usually discussed as real matrices, while unitary matrices are always complex. In that case, all the definitions for SO are the same, as is true for SU.