relation of eigenvalues and eigenvectors of inverse matrix

**saskadimova** · September 8th 2009, 08:52 PM

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

many thanks.

**NonCommAlg** · September 9th 2009, 05:34 AM

Originally Posted by saskadimova

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 ...

Thread: relation of eigenvalues and eigenvectors of inverse matrix

LinkBack

Thread Tools

Display

relation of eigenvalues and eigenvectors of inverse matrix

Similar Math Help Forum Discussions

What are the eigenvalues and eigenvectors of the following matrix?

eigenvalues/eigenvectors of a 3x3 matrix

Eigenvalues, Eigenvectors, Inverse matrix- am i on the right track?

[SOLVED] Eigenvalues and eigenvectors of a 3x3 matrix A? A unknown?

Eigenvectors and eigenvalues of a matrix

Search Tags