invariance of eigenvalues
Suppose $M$ is a $n\times n$ matrix. In the following proposition^{} when we say that “two matrices have the same spectra” we mean that the eigenvalues^{} coincide including multiplicity.

1.
If $S$ is an invertible matrix, then $M$ and ${S}^{1}MS$ have the same spectra.
Title  invariance of eigenvalues 

Canonical name  InvarianceOfEigenvalues 
Date of creation  20130322 15:17:29 
Last modified on  20130322 15:17:29 
Owner  matte (1858) 
Last modified by  matte (1858) 
Numerical id  5 
Author  matte (1858) 
Entry type  Definition 
Classification  msc 15A18 