In mathematics, the special unitary group of degree , denoted , is the Lie group of  unitary matrices with determinant 1 (i.e., real-valued determinant, not complex as for general unitary matrices). The group operation is that of matrix multiplication. The special unitary group is a subgroup of the unitary group , consisting of all unitary matrices. As a compact classical group, is the group that preserves the standard inner product on . It is itself a subgroup of the general linear group, .