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.

arXiv comment6 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

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• An optimum Hamiltonian for non-Hermitian quantum evolution and the complex Bloch sphere