# commuting matrices are simultaneously triangularizable

###### Theorem 1.

All matrices in the below are complex $n\times n$ matrices.
Let $A$,$B$ be matrices and $AB=BA$. Then there exists a unitary matrix $Q$ such that

$Q^{H}AQ=T_{1}$ , $Q^{H}BQ=T_{2}$

where ${}^{H}$ is the conjugate transpose and $T_{1},T_{2},$ are upper triangular matrices.

Title commuting matrices are simultaneously triangularizable CommutingMatricesAreSimultaneouslyTriangularizable 2013-03-22 15:26:48 2013-03-22 15:26:48 georgiosl (7242) georgiosl (7242) 12 georgiosl (7242) Theorem msc 15A23 SimultaneousUpperTriangularBlockDiagonalizationOfCommutingMatrices