Let GL ⁡ ⁡ ( n , C ) denote the group of n × × n invertible matrices with entries in C . Any closed subgroup of GL ⁡ ⁡ ( n , C ) is a Lie group; Lie groups of this sort are called matrix Lie groups. Since most of the interesting examples of Lie groups can be realized as matrix Lie groups, some textbooks restrict attention to this class, including those of Hall, Rossmann, and Stillwell. Restricting attention to matrix Lie groups simplifies the definition of the Lie algebra and the exponential map. The following are standard examples of matrix Lie groups.