Title: 22_1 Basic Concepts of Eigenvalues and Eigenvectors
Course: HELM Workbooks 2023-2024 > Section: HELM 22: Eigenvalues and Eigenvectors

From an applications viewpoint, eigenvalue problems are probably the most important problems that arise in connection with matrix analysis. In this Section we discuss the basic concepts.

We shall see that eigenvalues and eigenvectors are associated with square matrices of order \(n\times n\). If \(n\) is small (\(2\) or \(3\)), determining eigenvalues is a fairly straightforward process (requiring the solution of a low order polynomial equation). Obtaining eigenvectors is a little strange initially and it will help if you complete this preliminary quiz first.