On the Stable Perturbation and Nashed’s Condition for Generalized Inverses†

2020 ◽  
pp. 1-8
Author(s):  
Jiu Ding ◽  
Qianglian Huang
Keyword(s):  
Generalized Inverses ◽  
Stable Perturbation

On the uniform boundedness and convergence of generalized, Moore-Penrose and group inverses

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 5993-6003 ◽  
Author(s):  
Lanping Zhu ◽  
Changpeng Zhu ◽  
Qianglian Huang
Keyword(s):  
Operator Theory ◽  
Generalized Inverse ◽  
Matrix Theory ◽  
Uniform Boundedness ◽  
Generalized Inverses ◽  
Convergence Theorems ◽  
Linear Subspaces ◽  
Group Inverses ◽  
Stable Perturbation ◽  
The Relationship

This paper concerns the relationship between uniform boundedness and convergence of various generalized inverses. Using the stable perturbation for generalized inverse and the gap between closed linear subspaces, we prove the equivalence of the uniform boundedness and convergence for generalized inverses. Based on this, we consider the cases for the Moore-Penrose inverses and group inverses. Some new and concise expressions and convergence theorems are provided. The obtained results extend and improve known ones in operator theory and matrix theory.

Test matrices for generalized inverses

1978 ◽  
Vol 13 (4) ◽  
pp. 10-12 ◽  
Author(s):  
Gerhard Zielke
Keyword(s):  
Generalized Inverses ◽  
Test Matrices

Solving fuzzy linear systems using a block representation of generalized inverses: The group inverse

2018 ◽  
Vol 353 ◽  
pp. 66-85 ◽  
Author(s):  
Biljana Mihailović ◽  
Vera Miler Jerković ◽  
Branko Malešević
Keyword(s):  
Linear Systems ◽  
Generalized Inverses ◽  
Group Inverse ◽  
Fuzzy Linear Systems
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