Spectral perturbation by rank one matrices

2021/11/20 by Jon Merzel, Merzel, Jon, Ján Mináč +7
Computer Science · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Linear and multilinear algebra #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #matrix theory

paper · pdf · doi:10.48550/arxiv.2111.10624

openalex publication_date 2021/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a matrix of size n × n over an algebraically closed field F and q(t) a monic polynomial of degree n. In this article, we describe the necessary and sufficient conditions of q(t) so that there exists a rank one matrix B such that the characteristic polynomial of A+B is q(t).

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