On idempotency and tripotency of linear combinations of two commuting tripotent matrices

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2009

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Elsevier Science inc

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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Abstract

Let T-1 and T-2 be two nonzero commuting n x n tripotent matrices and c(1), c(2) two nonzero complex numbers. Necessary and sufficient conditions for the tripotency and the idempotency of c(1)T(1) + c(2)T(2) are obtained. The problems considered here have also statistical importance when c(1), c(2) are real scalars and T-1, T-2 are real symmetric matrices. (C) 2008 Elsevier Inc. All rights reserved.

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Özdemir, Halim/0000-0003-4624-437X; Güler, Nesrin/0000-0003-3233-5377
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Özdemir, Halim ORCID logo
Güler, Nesrin ORCID logo

Keywords

Idempotent matrix, Tripotent matrix, Quadratic form, Chi-square distribution, Diagonalization

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26

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Volume

207

Issue

1

Start Page

197

End Page

201

URI

https://doi.org/10.1016/j.amc.2008.10.017
 https://hdl.handle.net/20.500.14411/999

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