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

Toshiaki Tanaka
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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.

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Toshiaki Tanaka. 2006-05-24. On Existence of a Biorthonormal Basis Composed of Eigenvectors of Non-Hermitian Operators. https://doi.org/10.1088/0305-4470/39/24/012

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