Ikramov, Kh. D.; Chugunov, V. N. Diagonalizable matrices as a result of rank-one perturbations of nilpotent matrices. (English. Russian original) Zbl 1497.15012 Mosc. Univ. Comput. Math. Cybern. 46, No. 2, 76-80 (2022); translation from Vestn. Mosk. Univ., Ser. XV 2022, No. 2, 17-21 (2022). Summary: It is known that every normal matrix with a simple spectrum can be obtained by a rank-one perturbation of some nilpotent matrix \(N\). In this assertion, a normal matrix can actually be replaced by an arbitrary diagonalizable matrix. We determine the possible values of the index of nilpotency of the matrix \(N\). MSC: 15A20 Diagonalization, Jordan forms 15A18 Eigenvalues, singular values, and eigenvectors Keywords:diagonalizable matrix; nilpotent matrix; index of nilpotency; geometric multiplicity of eigenvalue PDFBibTeX XMLCite \textit{Kh. D. Ikramov} and \textit{V. N. Chugunov}, Mosc. Univ. Comput. Math. Cybern. 46, No. 2, 76--80 (2022; Zbl 1497.15012); translation from Vestn. Mosk. Univ., Ser. XV 2022, No. 2, 17--21 (2022) Full Text: DOI References: [1] Krupnik, M., Changing the spectrum of an operator by perturbation, Linear Algebra Appl., 167, 113-118 (1992) · Zbl 0762.15004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.