Every bounded operator 
acting on a Hilbert space 
has a decomposition 
, where 
and 
is a partial isometry. This decomposition is called polar
decomposition. If 
is invertible, then 
can be chosen to be unitary.
Polar Decomposition
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.Referenced on Wolfram|Alpha
Polar DecompositionCite this as:
Weisstein, Eric W., with contributions by Mohammad Sal Moslehian. "Polar Decomposition." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PolarDecomposition.html