Elements of Numerical Mathematical Economics with Excel

3.3. Eigenvalues and eigenvectors search: analytical and graphical approach

An important section of the theory of linear algebra is dedicated to finding the so-called eigenvalues (or characteristic values) and eigenvectors (or characteristic vectors). We will use them to solve the system of linear differential equations using the direct method (see Section 4.5).

Given a square matrix A of order n, the problem is to find the values of the parameter λ   such that the following is satisfied:

A x = λ x

(3.3-1)

Eq. (3.3-1) can be restated as follows:

A x − λ x = [ 0 ] ⇒ A x − λ I x = [ 0 ]

namely:

( A −