5Eigenvalues and eigenvectors

IA Vectors and Matrices

5 Eigenvalues and eigenvectors
Given a matrix A, an eigenvector is a vector x that satisfies Ax = λx for some
. We call
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.