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An algorithmic test for diagonalizability of finite-dimensional PT-invariant systems

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Publication details

JournalJournal of Physics A: Mathematical and General
DatePublished - 6 Jan 2006
Issue number1
Number of pages10
Pages (from-to)235-245
Original languageEnglish


A non-Hermitian operator does not necessarily have a complete set of eigenstates, contrary to a Hermitian 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.

Bibliographical note

© 2006 IOP Publishing Ltd. This is an author produced version of a paper published in Journal of Physics A: Mathematical and General.

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