From my reading, $SU(4)$ has 15 parameters and $SU(2)$ has 3 parameters that range differently with certain parameters (rotation angle). And all the parameters are linearly independent to each other.
My question are:
What the characteristic of each of the parameters?
If I choose two of them, what is the reason behind the theory?
Can anyone explain to me or suggest any book/paper to me to understand the parameters themselves?