Eigenvalues and eigenvectors of a matrix are of great importance in the qualitative as well as quantitative study of many physical problems. For example, stability of an aircraft is determined by the location of the eigenvalues of a certain matrix in the complex plane. Basic solutions of ordinary differential and difference equations with constant coefficients are expressed in terms of eigenvalues and eigenvectors of the coefficient matrices. In this chapter we shall mainly summarize properties of the eigenvalues and eigenvectors of matrices, which are of immense value.