relation of eigenvalues and eigenvectors of inverse matrix

• September 8th 2009, 08:52 PM
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.
• September 9th 2009, 05:34 AM
NonCommAlg
Quote:

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 ...