The spectrum of matrices depending on two idempotents
type: Item
instance of: scholarly article
title: The spectrum of matrices depending on two idempotents
zbMATH Open document ID: 1222.15014
author: Xiaoji Liu
author: Julio Benítez
published in: Applied Mathematics Letters
publication date: 2011-07-11T00:00:00Z
review text: The spectrum of the sum of idempotent matrices is studied. To be more precise, let \(P=P^2\) and \(Q=Q^2\) be idempotent matrices and \(a,b \in C\). Then the spectrum of \(aP+bQ\) can be related to the spectrum of \(P-Q, PQ, PQP\) and \(PQ-QP\). Here it is assumed that \(aP+bQ\) is diagonalizable. The results lead to simpler proofs of several results in the literature.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 5919232
zbMATH Keywords: spectrum
zbMATH Keywords: idempotent matrix
zbMATH Keywords: diagonalizable matrix
reviewed by: Ludwig Elsner
MaRDI profile type: Publication
full work available at URL: j.aml.2011.04.004
OpenAlex ID: W2030213370
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DOI: 10.1016/J.AML.2011.04.004
description: scientific article; zbMATH DE number 5919232