Let a, b, c, d be elements in a unital associative ring R. In this note, we generalize Cline?s formula for some new generalized inverses such as strong Drazin inverse, Hirano inverse and to the case when acd = dbd dba aca. As particular case, recent results are recovered.

A new algorithm is presented for the determination of the generalized inverse and the drazin inverse of a polynomial matrix. The proposed algorithms are based on the discrete Fourier transform and thus are computationally fast in contrast to other known algorithms. The above algorithms are implemented in the Mathematica programming language and illustrated via examples.

The reverse order law and the forward have been studied for various types of generalized inverses. $(b,c)$-inverse is a generalization some well known inverses, such as Moore-Penrose inverse, Drazin core etc. In this paper, $(b,c)$-inverse, in unital ring, investigated an equivalent condition to hold derived. Also, results on topic are generalized. Furthermore, ring with unity introduced, diffe...

In this paper we show how to apply Gröbner bases to compute the Drazin inverse of a matrix with multivariate rational functions as entries. When the coefficients of the rational functions depend on parameters, we give sufficient conditions for the Drazin inverse to specialize properly. In addition, we extend the method to weighted Drazin inverses. We present an empirical analysis that shows a g...

In this article we introduce a full-rank representation of the Drazin inverse AD of a given complex matrix A, which is based on an arbitrary full-rank decomposition of Al, l ≥ k, where k is the index of A. We show that the known representation of the Drazin inverse of A, devised in [7], represents a partial case of this result. Using this general representation, we introduce a determinantal rep...

†Department of Mathematics, Southeast University, Nanjing 210096, China ‡College of Mathematics and Information Science, Guangxi University, Nanning 530004, China E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] Abstract: It is well known that for an associative ring R, if ab is Drazin invertible then ba is Drazin invertible. In this case, (ba)D = b((ab)D)2a. This for...

In this article we extend the method of Yong-Lin Chen (Iterative methods for computing the generalized inverses A (2) T,S of a matrix A, Appl. Math. Comput. 75 (2-3) (1996)) to inifinite dimensional settings. Precisely, we construct an iterative method for computing outer generalized inverses of operators on Banach spaces, and also for computing the generalized Drazin inverse of Banach algebra ...

The aim of this work is to prove the existence and uniqueness Drazin inverse DMP inverses a bounded finite potent endomorphism. In particular, we give main properties these generalized inverses, offer their relationships with adjoint operator, study spectrum, compute respective traces determinants relate operator classical definitions inverse. Moreover, different Moore-Penrose are studied.

This paper deals with the algorithm for computing outer inverse with prescribed range and null space, based on the choice of an appropriate matrix G and Gauss–Jordan elimination of the augmented matrix [G | I]. The advantage of such algorithms is the fact that one can compute various generalized inverses using the same procedure, for different input matrices. In particular, we derive representa...