Special orthogonal group:SO(3,R)

Definition
This group, denoted $$SO(3,\R)$$, is the special orthogonal group for the standard dot product over the field of real numbers in three dimensions. Explicitly, it is given by:

$$\{ A \in GL(3,\R) \mid AA^T = \mbox{Identity matrix}, \det A = 1 \}$$

It is also isomorphic to the projective special unitary group $$PSU(2,\mathbb{C})$$ of degree two over the field of complex numbers, or equivalently, to the inner automorphism group of the group of unit quaternions.