The Drazin inverse of anti-triangular block matrices

Zhang, Daochang; Jin, Yu; Mosić, Dijana

doi:10.1007/s12190-021-01638-2

Cited by 6 publications

(2 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The sets of all Drazin invertible and group invertible operators of B(H) are denoted by B(H) D and B(H) # , respectively. Recent results about expressions for the Drazin inverse can be found in [19,20].…”

Section: Introductionmentioning

confidence: 99%

Inner-gMP and gMP-inner inverses

STOJANOVİC,

MOSİC

2024

Hacettepe Journal of Mathematics and Statistics

View full text Add to dashboard Cite

Solving some systems of operator equations, new kinds of generalized inverses are introduced. Since these new inverses can be expressed by inner and gMP inverses, they are called inner-gMP and gMP-inner inverses. In this way, the concepts of gMP, 1MP and MP1 inverses are generalized. Various representations and characterizations of inner-gMP and gMP-inner inverses are presented. Using the inner and *gMP inverse, we define the inner-*gMP and *gMP-inner inverses which are new extensions of 1MP, MP1 and *gMP inverses. We apply inner-gMP and gMP-inner inverses as well as inner-*gMP and *gMP-inner inverses to solve several kinds of linear equations. Consequently, we obtain solvability of the normal equation which is connected to the least--squares solution. Numerical examples are given to illustrate our results.

show abstract

Section: Introductionmentioning

confidence: 99%

Inner-gMP and gMP-inner inverses

STOJANOVİC,

MOSİC

2024

Hacettepe Journal of Mathematics and Statistics

View full text Add to dashboard Cite

show abstract

“…In [18,Theorem 2.3], Zhang and Mosić considered the g-Drazin inverse of M under the wider condition F EF π = 0. We refer the reader to [19,20,22] for further recent progresses on the Drazin and g-Drazin inverse of M. The motivation of this paper is to further study the generalized inverse of the block-operator matrix M under the condition F EF π = 0. In Section 2, we present the g-Drazin inverse for the operator matrix M under the condition EF EF π = 0 and F 2 EF π = 0, which extend [18,Theorem 2.3] to a wider case.…”

Section: Introductionmentioning

confidence: 99%