A square matrix U is a special unitary matrix if U U^* = I, where I is the identity matrix and U^* is the conjugate transpose matrix, and the determinant is det U = 1. The first condition means that U is a unitary matrix, and the second condition provides a restriction beyond a general unitary matrix, which may have determinant e^(i θ) for θ any real number.

antihermitian matrix | Hermitian inner product | special unitary group | unitary group | unitary matrix