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Polar Decomposition


Every bounded operator T acting on a Hilbert space H has a decomposition T=U|T|, where |T|=(T^*T)^(1/2) and U is a partial isometry. This decomposition is called polar decomposition. If T is invertible, then U can be chosen to be unitary.


This entry contributed by Mohammad Sal Moslehian

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References

Murphy, G. J. C-*-Algebras and Operator Theory. New York: Academic Press, 1990.

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Polar Decomposition

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Moslehian, Mohammad Sal. "Polar Decomposition." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/PolarDecomposition.html

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