A Matrix [[Lie groups]] is a Lie Group that is a subgroup of [[GL(n;F)]]. In order to identify what Lie Groups are also matrix Lie Groups we prove that a particular Lie Group is [isomorphic](Lie%20group%20isomorphisms.md) to a matrix Lie Group. A matrix Lie Group group fulfills [closure](closed%20set) such that a sequence $A_1 ... A_m$ in group $\mbox{G}$ converges to $A$ where $A \in \mbox{G}$, Otherwise $A$ is non-invertible, and thus it wouldn't be a subgroup of $\mbox{GL}(n,\mathbb{F})$ since invertibility is required for that to be the case. In the most general case, the dimensionality of the group is given by the number of elements, $n^2$ of the matrix, where the dimensionality may decrease as a result of additional constraints, such as with [[SL(n;R) and SL(n;C)]]. #MathematicalFoundations/Algebra/AbstractAlgebra/GroupTheory/Lie/LieGroups #MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/Operators/Matrices