Chapter 8 - Additional Applications

Abstract

Publisher Summary This chapter explores important uses of linear algebra in fields ranging from electronics to psychology. It also presents several additional practical applications of linear algebra in mathematics and science. It focuses on the uses of matrices to calculate the number of paths of a certain length among vertices of a graph or digraph. Multiplication of matrices is widely used in graph theory—a branch of mathematics that has come into prominence for modeling many situations in computer science, business, and the social sciences. Graphs and digraphs and introduced in the chapter and their relationship with matrices is examined. A digraph, or directed graph, is a special type of graph in which each edge is assigned a “direction.” It is also assumed assume that every time the words “graph” and “digraph” are used, they refer to “simple graphs” and “simple digraphs,” respectively. A simple graph is one having at most one edge between each pair of vertices. Similarly, a simple digraph is one having at most one edge in each direction between each pair of vertices. The pattern of edges among the vertices in a graph or digraph can be summarized in an algebraic way using matrices.