An Algorithmic Test for Diagonalizability of Finite-Dimensional PT-Invariant Systems
Quantum Physics
2015-06-26 v1
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.
Cite
@article{arxiv.quant-ph/0506042,
title = {An Algorithmic Test for Diagonalizability of Finite-Dimensional PT-Invariant Systems},
author = {Stefan Weigert},
journal= {arXiv preprint arXiv:quant-ph/0506042},
year = {2015}
}
Comments
13 pages, 1 figure