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[parent] invariance of eigenvalues (Definition)

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 $S^{-1} M S$ have the same spectra.



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Cross-references: invertible, multiplicity, eigenvalues, mean, proposition, matrix

This is version 2 of invariance of eigenvalues, born on 2005-05-20, modified 2008-10-22.
Object id is 7087, canonical name is InvarianceOfEigenvalues.
Accessed 1433 times total.

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AMS MSC: 15A18 (Linear and multilinear algebra; matrix theory :: Eigenvalues, singular values, and eigenvectors)
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