Further results on the (b, c)-inverse, the outer inverse AT,S(2) and the Moore–Penrose inverse in the Banach context

2018 ◽  
Vol 67 (5) ◽  
pp. 1006-1030 ◽  
Author(s):  
Enrico Boasso
Keyword(s):  
Outer Inverse

Condition number related to the outer inverse of a complex matrix

2009 ◽  
Vol 215 (8) ◽  
pp. 2826-2834 ◽  
Author(s):  
Dijana Mosić ◽  
Dragan S. Djordjević
Keyword(s):  
Condition Number ◽  
Complex Matrix ◽  
Outer Inverse

A note on the perturbation of an outer inverse

CALCOLO ◽  
2008 ◽  
Vol 45 (4) ◽  
pp. 263-273 ◽  
Author(s):  
Naimin Zhang ◽  
Yimin Wei
Keyword(s):  
Outer Inverse

Integral and limit representations of the outer inverse in Banach space

2012 ◽  
Vol 60 (3) ◽  
pp. 333-347 ◽  
Author(s):  
Xiaoji Liu ◽  
Yaoming Yu ◽  
Jin Zhong ◽  
Yimin Wei
Keyword(s):  
Banach Space ◽  
Outer Inverse

Outer inverse restricted by a linear system

2015 ◽  
Vol 63 (12) ◽  
pp. 2461-2493 ◽  
Author(s):  
Predrag S. Stanimirović ◽  
Dimitrios Pappas ◽  
Vasilios N. Katsikis ◽  
Marija S. Cvetković
Keyword(s):  
Linear System ◽  
Outer Inverse

scholarly journals The outer inverse f(2)T,S of a homomorphism of right R-modules

Filomat ◽  
2019 ◽  
Vol 33 (19) ◽  
pp. 6459-6468
Author(s):  
Zhou Wang
Keyword(s):  
Generalized Inverse ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Drazin Inverse ◽  
Group Inverse ◽  
Outer Inverse ◽  
Basic Properties ◽  
Definition Of ◽  
Necessary And Sufficient

In this paper, we introduce the definition of the generalized inverse f(2)T,S, which is an outer inverse of the homomorphism f of right R-modules with prescribed image T and kernel S. Some basic properties of the generalized inverse f(2)T,S are presented. It is shown that the Drazin inverse, the group inverse and the Moore-Penrose inverse, if they exist, are all the generalized inverse f 2) T,S. In addition, we give necessary and sufficient conditions for the existence of the generalized inverse f(1,2)T,S.

scholarly journals Rank Function and Outer Inverses

2018 ◽  
Vol 33 ◽  
pp. 16-23
Author(s):  
Manjunatha Prasad Karantha ◽  
K. Nayan Bhat ◽  
Nupur Nandini Mishra
Keyword(s):  
Commutative Ring ◽  
Linear Equations ◽  
Rank Function ◽  
Drazin Inverse ◽  
Rank Condition ◽  
Outer Inverse ◽  
The Matrix ◽  
Class Of Matrices ◽  
Necessary And Sufficient ◽  
Row Space

For the class of matrices over a field, the notion of `rank of a matrix' as defined by `the dimension of subspace generated by columns of that matrix' is folklore and cannot be generalized to the class of matrices over an arbitrary commutative ring. The `determinantal rank' defined by the size of largest submatrix having nonzero determinant, which is same as the column rank of given matrix when the commutative ring under consideration is a field, was considered to be the best alternative for the `rank' in the class of matrices over a commutative ring. Even this determinantal rank and the McCoy rank are not so efficient in describing several characteristics of matrices like in the case of discussing solvability of linear system. In the present article, the `rank--function' associated with the matrix as defined in [{\it Solvability of linear equations and rank--function}, K. Manjunatha Prasad, \url{http://dx.doi.org/10.1080/00927879708825854}] is discussed and the same is used to provide a necessary and sufficient condition for the existence of an outer inverse with specific column space and row space. Also, a rank condition is presented for the existence of Drazin inverse, as a special case of an outer inverse, and an iterative procedure to verify the same in terms of sum of principal minors of the given square matrix over a commutative ring is discussed.

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