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Elsevier Petik, T.; Ozdemir, H.; Benítez López, J. (2015). On the spectra of some combinations of two generalized quadratic matrices. Applied Mathematics and Computation. 978-990. doi:10.1016/j.amc.2015.06 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 = P A = A, (B − γQ)(B − δQ) = 0, BQ = QB = B, P Q = QP , AB = BA, and (A + B)(αβP − γδQ) = (αβP − γδQ)(A + B) with α, β, γ, δ ∈ . 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.

are reconsidered in different ways under the condition that the matrices involved in the linear combination are commutative. Thus, it is seen that there are some missing results in Theorem 2 in [1]. Then, by considering the obtained results and doing some detailed investigations, it is given a new characterization, without any restriction on the involved matrices except for commutativity, of a linear combination of an idempotent and a tripotent matrix that commute.

R, birimli, involutifleri sadece -1 ve 1 olan bir değişmeli halka ve M, elemanları R halkası üzerinden alınan bir üst üçgensel matrisler halkası olsun. Çalışmada, M halkasından alınan bir elemanın involutif olması için gerek ve yeter koşullar ortaya koyulmaktadır. Ayrıca, R sonlu olduğunda, M halkasındaki involutif elemanların sayısını belirleyen bir sonuç verilmekte ve bu sonuç sayısal örneklerle desteklenmektedir.