scholarly journals Reverse order law for reflexive generalized inverses of products of matrices

1998 ◽  
Vol 277 (1-3) ◽  
pp. 299-311 ◽  
Author(s):  
Alvaro R. De Pierro ◽  
Musheng Wei
Keyword(s):  
Generalized Inverses ◽  
Reverse Order ◽  
Reverse Order Law ◽  
Products Of Matrices

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.

scholarly journals The λ-Aluthge transform of EP matrices

Filomat ◽  
2018 ◽  
Vol 32 (12) ◽  
pp. 4403-4411 ◽  
Author(s):  
Dimitrios Pappas ◽  
Vasilios Katsikis ◽  
Predrag Stanimirovic
Keyword(s):  
Generalized Inverses ◽  
Reverse Order ◽  
Aluthge Transform ◽  
Reverse Order Law ◽  
Ep Matrix

In this work we present some relationships between an EP matrix T, its Aluthge transform ?(T) or the ?-Aluthge transform ??(T) and the Moore-Penrose inverse T+. We prove that the ?-Aluthge transform of T is also an EP matrix, and the same thing holds for ??(T)+ and ??(T+). Also, we explore the product ??(T)T, the connections between ?(T) and T+ as well as the reverse order law for generalized inverses which are associated with ??(T). Finally, it is verified that the ranges of T and ??(T) are equal in the case of EP matrices.

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