2 2]

Equation (2.10) is a system of homogeneous linear algebraic equations. Equation (2.10) is the classical form of an eigenproblem.

Chapter I is devoted to the solution of systems of nonhomogeneous linear algebraic equations:

Ax = b (2.12) As discussed in Section 1.I, Eq. (2.12) may have a unique solution (the case considered in Chapter I), no solution, an infinite number of solutions, or the trivial solution, x = 0, if the system of equations is homogeneous:

Ax = 0 (2.13) Chapter 2 is concerned with solutions to Eq. (2.13) other than x = 0, which are possible if the coefficient matrix A contains an unknown parameter, called an eigenvalue.