Results 1 to 10 of about 164 (146)

Representations for the Generalized Drazin Inverse of the Sum in a Banach Algebra and Its Application for Some Operator Matrices [PDF]

The Scientific World Journal, 2015
We investigate additive properties of the generalized Drazin inverse in a Banach algebra A. We find explicit expressions for the generalized Drazin inverse of the sum a+b, under new conditions on a,b∈A.
Xiaoji Liu, Xiaolan Qin
doaj   +2 more sources

Minimal Solution of Singular LR Fuzzy Linear Systems [PDF]

The Scientific World Journal, 2014
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.
M. Nikuie, M. Z. Ahmad
doaj   +2 more sources

The perturbation of Drazin inverse and dual Drazin inverse

Special Matrices
In this study, we derive the Drazin inverse (A+εB)D{\left(A+\varepsilon B)}^{D} of the complex matrix A+εBA+\varepsilon B with Ind(A+εB)>1{\rm{Ind}}\left(A+\varepsilon B)\gt 1 and Ind(A)=k{\rm{Ind}}\left(A)=k and the group inverse (A+εB)#{\left(A ...
Wang Hongxing, Cui Chong, Wei Yimin
doaj   +2 more sources

A Higher Order Iterative Method for Computing the Drazin Inverse [PDF]

The Scientific World Journal, 2013
A method with high convergence rate for finding approximate inverses of nonsingular matrices is suggested and established analytically. An extension of the introduced computational scheme to general square matrices is defined.
F. Soleymani, Predrag S. Stanimirović
doaj   +2 more sources

The Expression of the Drazin Inverse with Rank Constraints [PDF]

Journal of Applied Mathematics, 2012
By using the matrix decomposition and the reverse order law, we provide some new expressions of the Drazin inverse for any 2×2 block matrix with rank constraints.
Linlin Zhao
doaj   +3 more sources

On the Drazin Inverse of the Sum of Two Matrices

Journal of Applied Mathematics, 2011
We deduce the explicit expressions for (P+Q)D and (PQ)D of two matrices P and Q under the conditions P2Q=PQP and Q2P=QPQ. Also, we give the upper bound of |P+QD-PD|2.
Xiaoji Liu, Shuxia Wu, Yaoming Yu
doaj   +4 more sources

Minimal Rank Properties of Outer Inverses with Prescribed Range and Null Space

Mathematics, 2023
The purpose of this paper is to investigate solvability of systems of constrained matrix equations in the form of constrained minimization problems.
Dijana Mosić, Predrag S. Stanimirović, Spyridon D. Mourtas   +2 more
doaj   +1 more source

A Representation of the Drazin Inverse for the Sum of Two Matrices and the Anti-Triangular Block Matrices

Mathematics, 2023
In this paper, a new formula for the Drazin inverse for the Sum of Two Matrices is given under conditions weaker than those used in some current literature.
Li Guo, Guangli Hu, Deyue Yu, Tian Luan
doaj   +1 more source

B-Fredholm Spectra of Drazin Invertible Operators and Applications

Axioms, 2021
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.
Elvis Aponte, Jhixon Macías, José Sanabria, José Soto   +3 more
doaj   +1 more source

Differentiability of the g-Drazin inverse [PDF]

Studia Mathematica, 2005
Summary: If \(A(z)\) is a function of a real or complex variable with values in the space \(B(X)\) of all bounded linear operators on a Banach space \(X\) with each \(A(z)\) \(g\)-Drazin invertible, we study conditions under which the \(g\)-Drazin inverse \({A}^D(z)\) is differentiable.
Koliha, J. J., Rakočević, V.
openaire   +1 more source