In this paper, we investigate properties of  with closed range satisfying the operator equations   particular, invertibility of   with where Moore-Penrose inverse of T turns out to be usual under some classes operators. We also deduce a perturbed linear operator  where  such that  has ranges and  given conditions. The relation between and null s...

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

In this paper, some representations for the Moore-Penrose inverse of a linear combination of generalized and hypergeneralized projectors are found. Also, the invertibility for some linear combinations of commuting generalized and hypergeneralized projectors is considered.

The purpose of this paper is to introduce a new generalized inverse, called DMP inverse, associated with a square complex matrix using its Drazin and Moore-Penrose inverses. DMP inverse extends the notion of core inverse, introduced by O.M. Baksalary and G. Trenkler for matrices of index at most 1 in [Core inverse of matrices, Linear and Multilinear Algebra, 2010, 681–697] to matrices of an arb...

By a generalized inverse of a given matrix, we mean a matrix that exists for a larger class of matrices than the nonsingular matrices, that has some of the properties of the usual inverse, and that agrees with inverse when given matrix happens to be nonsingular. In theory, there are many different generalized inverses that exist. We shall consider the Moore Penrose, weighted Moore-Penrose, Draz...

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...

A simple formula for the group inverse of a 2× 2 block matrix with a bipartite digraph is given in terms of the block matrices. This formula is used to give a graph-theoretic description of the group inverse of an irreducible tridiagonal matrix of odd order with zero diagonal (which is singular). Relations between the zero/nonzero structures of the group inverse and the Moore-Penrose inverse of...

The symbolic Turiyam matrix is a whose entries contain Turiyam. Inverse matrices can generally be determined if the non-singular square matrix. Currently inverse of size m × n with 6= by Moore-Penrose inverse. purpose this research to determine algorithm on real n. Algebraic operations method used obtain applying algebraic concept inverses. main result obtained demonstration example given shows...