On Existence of a Biorthonormal Basis Composed of Eigenvectors of Non-Hermitian Operators

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.

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

References in corpus (1)

• Nonlinear Pseudo-Supersymmetry in the Framework of N-fold Supersymmetry

Cited by in corpus (2)

• Non-linear Supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties
• Pseudo-Hermiticity of an Exactly Solvable Two-Dimensional Model