Quantum Physics Division
Faculty of PhysicsAdam Mickiewicz University

Eigenvalues of functions of orthogonal projectors

O. M. Baksalary1 , G. Trenkler2

1 Faculty of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
2 Department of Statistics, Dortmund University of Technology, Vogelpothsweg 87, D-44221 Dortmund, Germany

Linear Algebra and Its Applications, 431, 2172-2186 (2009)


By representing two orthogonal projectors in a finite dimensional vector space as partitioned matrices, several characterizations concerning eigenvalues of various functions of the pair are obtained. These results substantially extend the ones already available in the literature. Additionally, some related results dealing with the functions of a pair of orthogonal projectors are provided, with the emphasis laying on the problem of invertibility.


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