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An Algorithmic Test for Diagonalizability of Finite-Dimensional PT-Invariant Systems

Stefan Weigert
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Abstract

A non-Hermitean operator does not necessarily have a complete set of eigenstates, contrary to a Hermitean one. An algorithm is presented which allows one to decide whether the eigenstates of a given PT-invariant operator on a finite-dimensional space are complete or not. In other words, the algorithm checks whether a given PT-symmetric matrix is diagonalizable. The procedure neither requires to calculate any single eigenvalue nor any numerical approximation.

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Stefan Weigert. 2005-06-06. An Algorithmic Test for Diagonalizability of Finite-Dimensional PT-Invariant Systems. https://doi.org/10.1088/0305-4470/39/1/017

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