Some Applications of Matrices and Graphs in Euclidean Geometry

This chapter presents some facts and examples illustrating the interplay between matrix theory, graph theory, and n-dimensional Euclidean geometry. The main objects of Euclidean geometry are, of course, the points. The simplest way of introducing them is to identify points with the endpoints of vectors; formally, one introduces an artificial point, the origin O, and the points are sums of this origin with any vector. A more general treatment of Euclidean n-space can be found in Chapter 65.