The notation "GL(n, ℝ)" refers to the general linear group of degree n over the real numbers. This group consists of all n x n invertible matrices with real entries. An invertible matrix is one that has a non-zero determinant, meaning it can be used to solve systems of linear equations uniquely. The elements of GL(n, ℝ) play a crucial role in various fields, including linear algebra, geometry, and physics. They represent transformations that can be applied to vectors in n-dimensional space, preserving the structure of the space while allowing for scaling, rotation, and other manipulations.