The Characterizations of WG Matrix and Its Generalized Cayley–Hamilton Theorem

Based on the core-EP decomposition, we use the WG inverse, Drazin inverse, and other inverses to give some new characterizations of the WG matrix. Furthermore, we generalize the Cayley–Hamilton theorem for special matrices including the WG matrix. Finally, we give examples to verify these results.

State-Feedback Control in Descriptor Discrete-Time Fractional-Order Linear Systems: A Superstability-Based Approach

In this article, the superstabilizing state-feedback control problem in descriptor discrete-time fractional-order linear (DDFL) systems with a regular matrix pencil is studied. Methods for investigating the stability and superstability of the considered class of dynamical systems are presented. Procedures for the computation of the static state-feedback (SSF) and dynamic state-feedback (DSF) gain matrices such that the closed-loop DDFL (CL-DDFL) system is superstable are presented. A numerical example is used to show the efficacy of the presented approach. Our considerations were based on the Drazin inverse matrix method.

B-Fredholm Spectra of Drazin Invertible Operators and Applications

In this article, we consider Drazin invertible operators for study of the relationship between their B-Fredholm spectra and the transfer between some of the spectral properties defined through B-Fredholm spectra of this class of operators. Among other results, we investigate the transfer of generalized a-Weyl’s theorem from T to their Drazin inverse S, if it exists.

The W-weighted Drazin-star matrix and its dual

After decades studying extensively two generalized inverses, namely Moore--Penrose inverse and Drazin inverse, currently, we found immersed in a new generation of generalized inverses (core inverse, DMP inverse, etc.). The main aim of this paper is to introduce and investigate a matrix related to these new generalized inverses defined for rectangular matrices. We apply our results to the solution of linear systems.

Drazin inverse: representation, approximation, continuity and illustrations

In this paper, we present some characteristics and expressions of the Drazin inverse for matrices and bounded linear operators in Banach spaces. We give a survey of some of results on the continuity of the Moore-Penrose and Drazin inverse, direct technics for computing the Drazin inverse are discussed, they are based on Euler-Knopp Method and characterized in terms of a limiting process. The examples presented are for illustrative purposes, some of which are provided for testing the considered iterative processes