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

Weigert, S. (2006) An algorithmic test for diagonalizability of finite-dimensional PT-invariant systems. Journal of Physics A: Mathematical and General. pp. 235-245. ISSN 0305-4470

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Abstract

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.

Item Type:	Article
Copyright, Publisher and Additional Information:	© 2006 IOP Publishing Ltd. This is an author produced version of a paper published in Journal of Physics A: Mathematical and General.
Keywords:	SYMMETRIC QUANTUM-MECHANICS, OPERATOR
Academic Units:	The University of York > Mathematics (York)
Depositing User:	Repository Officer
Date Deposited:	22 Jun 2006
Last Modified:	19 Feb 2013 11:44
Published Version:	http://dx.doi.org/10.1088/0305-4470/39/1/017
Status:	Published
Refereed:	Yes
Related URLs:	http://www-users.york.ac.uk/~slow500/Pub... http://dx.doi.org/10.1088/0305-4470/39/1...
URI:	http://eprints.whiterose.ac.uk/id/eprint/1334

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