On the spectra of some combinations of two generalized quadratic matrices

Abstract

[EN] 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 − γ Q)(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. © 2015 Elsevier Inc. All rights reserved.