On the spectra of some combinations of two generalized quadratic matrices

Tuǧba Petik, Halim Özdemir and Julio Benítez

Applied Mathematics and Computation, 2015, vol. 268, issue C, 978-990

Abstract: Let A and B be two generalized quadratic matrices with respect to idempotent matrices P and Q, respectively, such that (A−αP)(A−βP)=0,AP=PA=A,(B−γQ)(B−δQ)=0,BQ=QB=B,PQ=QP,AB ≠ BA, and (A+B)(αβP−γδQ)=(αβP−γδQ)(A+B) with α,β,γ,δ∈C. Let A+B be diagonalizable. The relations between the spectrum of the matrix A+B and the spectra of some matrices produced from A and B are considered. Moreover, some results on the spectrum of the matrix A+B are obtained when A+B is not diagonalizable. Finally, some results and examples illustrating the applications of the results in the work are given.

Keywords: Quadratic matrix; Generalized quadratic matrix; Idempotent matrix; Spectrum; Linear combination; Diagonalization (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:268:y:2015:i:c:p:978-990

DOI: 10.1016/j.amc.2015.06.093

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