Random Rotations

Rotations are among the simplest and most important of linear operations, and the group of rotations is a fundamental structure both for physics and geometry. In the article, we present an introductory discussion about random rotations, which can be seen as an example from the more general theory of random operators or random matrices, area which finds countless applications. We discuss the structure of the orthogonal group. an algorithm for generating random rotations and results for the probability distributions of matrix elements and eigenvalues.