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

S. Weigert

doi:10.1088/0305-4470/39/1/017

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

S. Weigert

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	235-245
Number of pages	10
Journal	Journal of Physics A: Mathematical and General
Volume	39
Issue number	1
DOIs	https://doi.org/10.1088/0305-4470/39/1/017
Publication status	Published - 6 Jan 2006

Bibliographical note

Keywords

SYMMETRIC QUANTUM-MECHANICS
OPERATOR

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10.1088/0305-4470/39/1/017

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Cite this

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