In this article, we discuss the group inverse of aP+ bQ+ cPQ+ dQP+ ePQP+ fQPQ+ gPQPQ
of idempotent matrices P and Q, where a, b, c, d, e, f, g∈ ℂ and a≠ 0, b≠ 0, put forward its …

Let T1 and T2 be two nonzero commuting n× n tripotent matrices and c1, c2 two nonzero
complex numbers. Necessary and sufficient conditions for the tripotency and the …

The Drazin inverse of the linear combinations of two idempotents in the Banach algebra Page
1 Linear Algebra and its Applications 436 (2012) 3132–3138 Contents lists available at …

Let R be an associative ring with identity 1. We describe all idempotent matrices with only
zeros and ones on the diagonal in T (n, R)–the ring of n× n upper triangular matrices over R …

Let and be nonzero quadratic matrices and let and be nonzero complex numbers.
Necessary and sufficient conditions for the quadraticity of the linear combinations of the form …

It is investigated the necessary and sufficient conditions for the generalized quadraticity of a
linear combination of any two generalized quadratic matrices. The main result obtained is, in …

begin {abstract} The relations between the spectrum of the matrix $ Q+ R $ and the spectra
of the matrices $(gamma+ delta) Q+ (alpha+ beta) R-QR-RQ $, $ QR-RQ $, $ alpha beta R …

Let and be two nonzero commuting and-quadratic matrices, respectively, where with and.
The aim of this work is mainly to characterize all situations, where the linear combination is a …

This paper deals with idempotent operators (ie, P2= P) and n-potent operators (ie, Pn= P).
We characterize the invertibility, the group invertibility and idempotency of the linear …

This paper concerns with the tripotency of a linear combination of three matrices, which has
a background in statistical theory. We demonstrate all the possible cases that lead to the …