# Thread: relation of eigenvalues and eigenvectors of inverse matrix

1. ## relation of eigenvalues and eigenvectors of inverse matrix

What is the relation between the eigenvalues and the eigenvectors of a matrix and its inverse?

many thanks.

a square matrix A is invertible if and only all its eigenvalues are non-zero. now $Ax = \lambda x$ if and only if $A^{-1}x=\frac{1}{\lambda} x.$ thus ...