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

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

2005-06-06

arxiv.org/abs/quant-ph/0506042v1

J. Phys. A 39 (2006) 235

Physics

Quantum Physics

13 pages, 1 figure

Scientific paper

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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