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%%% Primary Title: Schur decomposition
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%%% Owner: Daume
%%% Author(s): Daume
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 If $A$ is a \htmladdnormallink{complex}{http://planetmath.org/encyclopedia/PolarForm.html} \htmladdnormallink{square matrix}{http://planetmath.org/encyclopedia/SquareMatrix.html} of \htmladdnormallink{order}{http://planetmath.org/encyclopedia/Order7.html} n \textit{(i.e. $A\in\mathrm{Mat}_n(\mathbb{C})$)}, then there exists a \htmladdnormallink{unitary matrix}{http://planetmath.org/encyclopedia/UnitaryMatrix.html} $Q \in \mathrm{Mat}_n(\mathbb{C})$ such that\\
\begin{center}
$Q^HAQ = T = D + N$
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where $^H$ is the \htmladdnormallink{conjugate transpose}{http://planetmath.org/encyclopedia/Tranjugate.html}, $D = \operatorname{diag}(\lambda_1,   \dots, \lambda_n)$ \textit{(the $\lambda_i$ are \htmladdnormallink{eigenvalues}{http://planetmath.org/encyclopedia/Eigenvalues.html} of $A$)}, and $N \in \mathrm{Mat}_n(\mathbb{C})$ is \htmladdnormallink{strictly upper triangular matrix}{http://planetmath.org/encyclopedia/StrictlyLowerTriangularMatrix.html}. Furthermore, $Q$ can be chosen such that the eigenvalues $\lambda_i$ appear in any order along the \htmladdnormallink{diagonal}{http://planetmath.org/encyclopedia/Diagonal.html}. \cite{1}
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\bibitem[GVL]{1} Golub, H. Gene, Van Loan F. Charles:  Matrix Computations \textit{(Third Edition)}.  The Johns Hopkins University Press, London, 1996.
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