The notation "SO(n, R)" refers to the special orthogonal group in n dimensions over the real numbers. This group consists of all n x n orthogonal matrices with a determinant of 1. Orthogonal matrices preserve lengths and angles, making them essential in various applications, including computer graphics and physics. The elements of SO(n, R) represent rotations in n-dimensional space. These rotations can be visualized as transformations that maintain the structure of geometric objects. The group is fundamental in areas such as linear algebra, differential geometry, and theoretical physics, particularly in the study of symmetries and conservation laws.