TOPICS
Search

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

Explore with Wolfram|Alpha

References

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

Referenced on Wolfram|Alpha

Polar Decomposition

Cite this as:

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

Subject classifications