2006/03/31 by Toshiaki Tanaka
Computer Science · Mathematics · Physics and Astronomy · #Basis (linear algebra) #Defective matrix #Eigenvalues and eigenvectors #Generalization #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Modal matrix #Operator theory #Set (abstract data type) #Spectral Theory in Mathematical Physics #math-ph #math.FA #math.MP #quant-ph
paper · pdf · doi:10.1088/0305-4470/39/24/012
published as J. Phys. A: Math. Gen. 39 (2006) 7757-7761 · 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
arxiv created 2006/05/24 · openalex publication_date 2006/05/31 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.