Idempotency of linear combinations of an idempotent matrix and a tripotent matrix
type: Item
instance of: scholarly article
title: Idempotency of linear combinations of an idempotent matrix and a tripotent matrix
zbMATH Open document ID: 1016.15027
DOI: 10.1016/S0024-3795(02)00343-9
author: Jerzy K. Baksalary
author: Oskar Maria Baksalary
author: George P. H. Styan
published in: Linear Algebra and its Applications
publication date: 2003-02-05T00:00:00Z
review text: Let \(A\) be a matrix with entries in the complex numbers. Then \(A\) is called idempotent if \(A^2=A\), it is called tripotent if \(A^3=A.\) If \(B_1\) and \(B_2\) are nonzero idempotent matrices, then \(B=B_1-B_2\) is called essentially tripotent. Suppose \(A\) is idempotent, \(B\) is essentially tripotent, and \(c_1,c_2\neq 0.\) The authors determine when a linear combination \(c_1A+c_2B\) is idempotent.
reviewed by: Erich W. Ellers
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 62H10
Mathematics Subject Classification ID: 15A63
zbMATH DE Number: 1864711
zbMATH Keywords: projector
zbMATH Keywords: quadratic form
zbMATH Keywords: \(\chi^2\) distribution
zbMATH Keywords: idempotency
zbMATH Keywords: idempotent matrix
zbMATH Keywords: tripotent matrix
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1864711