On idempotency and tripotency of linear combinations of two commuting tripotent matrices
type: Item
instance of: scholarly article
title: On idempotency and tripotency of linear combinations of two commuting tripotent matrices
zbMATH Open document ID: 1167.15019
author: H. Özdemir
author: M. Sarduvan
author: Ahmet Yaşar Özban
author: Nesrin Güler
published in: Applied Mathematics and Computation
publication date: 2009-03-02T00:00:00Z
review text: Let \(T_{1}\) and \(T_{2}\) be two nonzero complex \({n}\times{n}\) matrices. Further let \(T_{1}\) and \(T_{2}\) be commuting tripotent, i.e. \(T_{1}T_{2}=T_{2}T_{1}\) and \(T_{i}^{3}=T_{i}\), \({i=1,2}\). Now for two complex numbers \(\lambda_{1}\) and \(\lambda_{2}\), put \({T}=\lambda_{1}T_{1}+\lambda_{2}T_{2}\). The authors present necessary and sufficient conditions for the tripotency and the idempotency of \(T\). They discuss the statistical importance of the results as well. They finish their paper by presenting some examples.
reviewed by: Manouchehr Misaghian
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A27
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 62E99
zbMATH DE Number: 5522203
zbMATH Keywords: idempotent matrix
zbMATH Keywords: tripotent matrix
zbMATH Keywords: quadratic form
zbMATH Keywords: chi-square distribution
zbMATH Keywords: diagonalization
MaRDI profile type: Publication
full work available at URL: j.amc.2008.10.017
OpenAlex ID: W2030385829
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cites work: Matrix Analysis
DOI: 10.1016/J.AMC.2008.10.017
description: scientific article; zbMATH DE number 5522203