Fundamental Eigenvectors

Abstract

In Section 1–2.1, we described a problem in the control of industrial processes which gives rise to the eigenvector-eigenvalue problem or eigenproblem for short. We shall now begin our study of this problem, for the case when E_l is a (linear) blog. If A εℳ_nn is a square matrix, we shall say that x ε E_n is an eigenvector of A and λ ε E_l a corresponding eigenvalue of A if there holds:

$$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{A}\otimes\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{x}=\lambda\otimes\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{x}$$

(23-1)