# 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 CommutingNormalMatricesAreSimultaneouslyDiagonalizable 2013-03-22 15:26:51 2013-03-22 15:26:51 georgiosl (7242) georgiosl (7242) 7 georgiosl (7242) Corollary msc 15A23