Publisher Summary This chapter focuses on eigenvalues and eigenvectors. In general, it is very difficult to find the eigenvalues of a matrix. First, the characteristic equation must be obtained. For the matrices of high order, this in itself is a lengthy task. Once the characteristic equation is determined, it must be solved for its roots. If the equation is of the high order, this can be an impossibility in practice. To each distinct eigenvalue of a matrix A, there will correspond at least one eigenvector that can be found by solving an appropriate set of homogeneous equations. Even if a mistake is made in finding the eigenvalues of a matrix, the error will become apparent when the eigenvector corresponding to the incorrect eigenvalue is found. By definition, an eigenvector can not be the zero vector. The trace of a matrix A, designated by tr(A), is the sum of the elements on the main diagonal.