On the diagonal of the matrices in a similarity class

2012/07/03 by Clément de Seguins Pazzis, Pazzis, Clément de Seguins
Agricultural and Biological Sciences · Computer Science · Engineering · Mathematics · #15A21 #15A29 #Advanced Scientific Research Methods #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #graph theory and CDMA systems #math.RA #msc:15A21 #msc:15A29

paper · pdf · doi:10.48550/arxiv.1207.0631

4 pages, withdrawn since the result has already been published with a similar proof

openalex publication_date 2012/07/03 · arxiv created 2012/08/29 · arxiv updated 2012/08/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let A be an n by n matrix with entries in an arbitrary field, and c₁,...,c_n be scalars. We prove that if A is not a scalar multiple of the identity matrix, then the condition c₁+...+c_n=tr(A) is necessary and sufficient for A to be similar to a matrix with diagonal entries c₁,...,c_n.

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