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Polar decomposition
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===Relation to normal matrices=== The matrix <math>A</math> with polar decomposition <math>A = UP</math> is [[normal matrix|normal]] if and only if <math>U</math> and <math>P</math> [[Commuting matrices|commute]] (<math>UP = PU</math>), or equivalently, they are [[Diagonalizable matrix#Simultaneous diagonalization|simultaneously diagonalizable]].
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