On Existence of a Biorthonormal Basis Composed of Eigenvectors of Non-Hermitian Operators
Quantum Physics
2007-05-23 v3 Mathematical Physics
Functional Analysis
math.MP
Abstract
We present a set of necessary conditions for the existence of a biorthonormal basis composed of eigenvectors of non-Hermitian operators. As an illustration, we examine these conditions in the case of normal operators. We also provide a generalization of the conditions which is applicable to non-diagonalizable operators by considering not only eigenvectors but also all root vectors.
Keywords
Cite
@article{arxiv.quant-ph/0603075,
title = {On Existence of a Biorthonormal Basis Composed of Eigenvectors of Non-Hermitian Operators},
author = {Toshiaki Tanaka},
journal= {arXiv preprint arXiv:quant-ph/0603075},
year = {2007}
}
Comments
6 pages, no figures; (v2) minor revisions based on the comment quant-ph/0603096; (v3) presentation improved, final version to appear in Journal of Physics A