U(n) refers to the group of all n x n unitary matrices, which are complex square matrices that preserve the inner product. This means that when a unitary matrix is multiplied by its conjugate transpose, the result is the identity matrix. Unitary matrices play a crucial role in quantum mechanics and various fields of mathematics, particularly in linear algebra. The notation U(n) indicates that the group consists of matrices of size n, where n can be any positive integer. The structure of U(n) is important in areas such as quantum computing, signal processing, and representation theory, as it helps describe symmetries and transformations in complex vector spaces.