5 Eigenvalues and eigenvectors

Given a matrix A, an eigenvector is a vector x that satisfies Ax = λx for some

λ

. We call

λ

the associated eigenvalue. In some sense, these vectors are not

modified by the matrix, and are just scaled up by the matrix. We will look

at the properties of eigenvectors and eigenvalues, and see their importance in

diagonalizing matrices.