Unitary similarity of projectors

@article{Dokovic1991UnitarySO,
  title={Unitary similarity of projectors},
  author={Dragomir Z. Dokovic},
  journal={aequationes mathematicae},
  year={1991},
  volume={42},
  pages={220-224}
}
  • D. Dokovic
  • Published 1 August 1991
  • Mathematics
  • aequationes mathematicae
SummaryWe deal with linear operators acting in a finite dimensional complex Hilbert space. We show that there exists a simple canonical form for projectors (not necessarily orthogonal) under unitary similarity. As a consequence we obtain a simple test for unitary similarity of projectors. IfP is a projector we show thatP andP* are unitarily similar. We also determine the isomorphism type of the algebra generated by the projectorsP andP*. 
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References

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On unitary similarity of matrices
A COMPLETE SET OF UNITARY INVARIANTS FOR OPERATORS GENERATING FINITE W -ALGEBRAS OF TYPE I