Mathematically, the n-order unitary group is a group composed of n×n unitary matrices, and group multiplication is matrix multiplication. Unitary group, denoted as U(n), is a subgroup of general linear group GL(n, c). In the simplest case, n = 1, and the group U( 1) is equivalent to a cyclic group, which is formed by multiplying all complex numbers with an absolute value of 1. All unitary groups contain one such subgroup. Unitary group U(n) is an n2-dimensional real Lie group. The Lie algebra of U(n) consists of all complex n× n oblique Hermite matrices, and the Lie brackets are commutators. General unitary groups (also called unitary similar groups) make A * A a non-zero complex number of identity matrix of all complex matrices A, which is the product of unitary groups and positive multiples of identity matrix.