# 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. 1.

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

Title invariance of eigenvalues InvarianceOfEigenvalues 2013-03-22 15:17:29 2013-03-22 15:17:29 matte (1858) matte (1858) 5 matte (1858) Definition msc 15A18