scholarly journals On Generalized Inverses, Group Inverses And Reverse Order Law For Range Quaternion Hermitian Matrices (Q-Ep)

2016 ◽  
Vol 12 (04) ◽  
pp. 51-55
Author(s):  
Dr.K. Gunasekaran ◽  
S. Sridevi
Keyword(s):  
Generalized Inverses ◽  
Reverse Order ◽  
Hermitian Matrices ◽  
Reverse Order Law ◽  
Group Inverses

On the group invertibility of operators

2016 ◽  
Vol 31 ◽  
pp. 492-510
Author(s):  
Chunyuan Deng
Keyword(s):  
Hilbert Spaces ◽  
Main Topic ◽  
Reverse Order ◽  
Operator Matrices ◽  
Reverse Order Law ◽  
Block Operator ◽  
Block Operator Matrices ◽  
Group Inverses ◽  
Triangular Block ◽  
Equivalent Conditions

The main topic of this paper is the group invertibility of operators in Hilbert spaces. Conditions for the existence of the group inverses of products of two operators and the group invertibility of anti-triangular block operator matrices are studied. The equivalent conditions related to the reverse order law for the group inverses of operators are obtained.

scholarly journals Some additive and multiplicative results for generalized inverses

Filomat ◽  
2015 ◽  
Vol 29 (9) ◽  
pp. 2049-2057
Author(s):  
Jovana Nikolov-Radenkovic
Keyword(s):  
Hilbert Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Generalized Inverses ◽  
Reverse Order ◽  
Reverse Order Law ◽  
Necessary And Sufficient ◽  
Regular Operators

In this paper we give necessary and sufficient conditions for A1{1,3} + A2{1, 3}+ ... + Ak{1,3} ? (A1 + A2 + ... + Ak){1,3} and A1{1,4} + A2{1,4} + ... + Ak{1,4} ? (A1 + A2 + ... + Ak){1,4} for regular operators on Hilbert space. We also consider similar inclusions for {1,2,3}- and {1,2,4}-i inverses. We give some new results concerning the reverse order law for reflexive generalized inverses.

Generalized Inverses

2021 ◽  
Vol 22 ◽  
pp. 13-32
Author(s):  
Dragan S. Djordjevic
Keyword(s):  
Generalized Inverses ◽  
Drazin Inverse ◽  
Reverse Order ◽  
Survey Paper ◽  
Reverse Order Law

In this survey paper we present some aspects of generalized inverses, which are related to inner and outer invertibility, Moore-Penrose inverse, the appropriate reverse order law, and Drazin inverse.

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