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Linear and Multilinear Algebra Volume 61, 2013 - Issue 4
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Original Articles

On nonsingularity of combinations of three group invertible matrices and three tripotent matrices

Julio Benítez Departamento de Matemática Aplicada, Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, SpainCorrespondence[email protected]
,
Murat Sarduvan Department of Mathematics, Sakarya University, TR54187 Sakarya, Turkey
,
Sedat Ülker Osmancιk Ömer Derindere Vacotional School, Hitit University, TR19500 Çorum, Turkey
&
Halim Özdemir Department of Mathematics, Sakarya University, TR54187 Sakarya, Turkey
Pages 463-481 | Received 19 Dec 2011, Accepted 11 Apr 2012, Published online: 11 Jun 2012
 
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Abstract

Let T = c 1 T 1 + c 2 T 2 + c 3 T 3 − c 4(T 1 T 2 + T 3 T 1 + T 2 T 3), where T 1, T 2, T 3 are three n × n tripotent matrices and c 1, c 2, c 3, c 4 are complex numbers with c 1, c 2, c 3 nonzero. In this article, necessary and sufficient conditions for the nonsingularity of such combinations are established and some formulae for the inverses of them are obtained. Some of these results are given in terms of group invertible matrices.

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Acknowledgments

We would like to thank the referee for his/her careful reading. The first author was supported by the Vicerrectorado de Investigación U.P.V. PAID 06-2010-2285.

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