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

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

2006-03-09

arxiv.org/abs/quant-ph/0603075v3

J. Phys. A: Math. Gen. 39 (2006) 7757-7761

Physics

Quantum Physics

6 pages, no figures; (v2) minor revisions based on the comment quant-ph/0603096; (v3) presentation improved, final version to

Scientific paper

10.1088/0305-4470/39/24/012

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.

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