Advanced Engineering Mathematics, 7th Edition

8.8 Eigenvalue Problem

INTRODUCTION

If A is an n × n matrix and K is an n × 1 matrix (column vector), then the product AK is defined and is another n × 1 matrix. It is important in many applications to determine whether there exist nonzero n × 1 matrices K such that the product vector AK is a constant multiple λ of K itself. The problem of solving AK = λK for nonzero vectors K is called the eigenvalue problem for the matrix A.

A Definition

The foregoing introductory remarks are summarized in the next definition.

DEFINITION 8.8.1 Eignvalues and Eigenvectors

Let A be an n × n matrix. A number λ is said to be an eigenvalue of A if there ...