ABSTRACT
This chapter deals with an introductory study of the eigenvalues and eigenvectors of square matrices which represents an important branch of linear algebra. Eigenvalue problems arise in a great variety of ways which are often related to oscillation problems. In such cases the eigenvalues characterize the frequencies of oscillation of a system, and the eigenvectors then describe its corresponding modes of oscillation. The chapter describes a brief introduction to some of the applications of matrices, including the use of linear transformations in computer graphics and the numerical solution of the Laplace equation in the context of the temperature distribution in a metal. It introduces the fundamental ideas connected with matrices and their algebra, and explores proceed quickly through the basic definitions and theorems. If the truss is in equilibrium, the algebraic sum of all the forces acting on the truss in both the horizontal and vertical directions must be zero, as must be the algebraic sum of all the moments.
