The [matrix Lie group](Matrix%20Lie%20group.md), $U(n)$ is a subgroup of [[GL(n;F)]] containing $n \times n$ [unitary matrices](Unitary%20operators.md#Unitary%20matrices). ^ea2bd5 # Lie algebras of $\mathrm{U}(n)$ The [Lie algebra](Lie%20algebras.md) of $U(n)$ consists of all matrices with complex elements such that $X^{\dagger} = -X$. #MathematicalFoundations/Algebra/AbstractAlgebra/GroupTheory/Lie/LieGroups/Algebras/LieAlgebras #MathematicalFoundations/Algebra/AbstractAlgebra/GroupTheory/Lie/LieGroups