Unitary similarity of projectors
- Cite this article as:
- Doković, D.Ž. Aeq. Math. (1991) 42: 220. doi:10.1007/BF01818492
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We 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*.