# commuting normal matrices are simultaneously diagonalizable

All matrices in the below are complex $n\times n$ matrices.

Let $A$,$B$ be normal matrices^{}, $AB=BA$. Then there exists a unitary matrix^{} $Q$ such that

${Q}^{H}AQ={D}_{1}$ , ${Q}^{H}BQ={D}_{2}$

where ${}^{H}$ is the conjugate transpose^{} and ${D}_{1},{D}_{2}$ are diagonal matrices^{}.

Title | commuting normal matrices are simultaneously diagonalizable |
---|---|

Canonical name | CommutingNormalMatricesAreSimultaneouslyDiagonalizable |

Date of creation | 2013-03-22 15:26:51 |

Last modified on | 2013-03-22 15:26:51 |

Owner | georgiosl (7242) |

Last modified by | georgiosl (7242) |

Numerical id | 7 |

Author | georgiosl (7242) |

Entry type | Corollary |

Classification | msc 15A23 |