In this paper, the singular LR fuzzy linear system is introduced. Such systems are divided into two parts: singular consistent LR fuzzy linear systems and singular inconsistent LR fuzzy linear systems. The capability of the generalized inverses such as Drazin inverse, pseudoinverse, and {1}-inverse in finding minimal solution of singular consistent LR fuzzy linear systems is investigated.

In this paper, we use the Drazin inverse to derive some new equivalences of the reverse order law for the group inverse in unitary rings. Moreover, if the ring has an involution, we present more equivalences when both involved elements are EP.

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.

In this article we characterize operators on Banach spaces which have the same projections related to their outer or inner generalized inverses. As corollaries, we obatin well-known results for the Drazin inverse of bounded operators.

Abstract The aim of this work is to extend bounded finite potent endomorphisms on arbitrary Hilbert spaces the notions Drazin-Star and Star-Drazin matrices that have been recently introduced by D. Mosi?. existence, structure main properties these operators are given. In particular, we obtain new a complex matrix. Moreover, explicit solutions some infinite linear systems from inverse endomorphis...

The purpose of this paper is to investigate solvability systems constrained matrix equations in the form minimization problems. main novelty unification solutions considered with corresponding For a particular case we extend some well-known results and give several new for weak Drazin inverse. characterizations inverse, group inverse Moore–Penrose are obtained as consequences.

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 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.

In 1979, Campbell and Meyer proposed the problem of finding a formula for the Drazin inverse of a 2 × 2 matrix M = [ A B C D ] in terms of its various blocks, where the blocks A and D are required to be square matrices. Special cases of the problems have been studied. In particular, a representation of the Drazin inverse of M , denoted by MD , has recently been obtained under the assumptions th...