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	2013-03-22 15:17:29
Last modified on	2013-03-22 15:17:29
Owner	matte (1858)
Last modified by	matte (1858)
Numerical id	5
Author	matte (1858)
Entry type	Definition
Classification	msc 15A18