Mixed-type reverse order laws for generalized inverses in rings with involution

2013 ◽  
Vol 82 (3-4) ◽  
pp. 641-650
Author(s):  
DIJANA MOSIC ◽  
DRAGAN S. DJORDJEVIC
Keyword(s):  
Mixed Type ◽  
Generalized Inverses ◽  
Reverse Order ◽  
Rings With Involution

Mixed-type reverse order laws for the group inverses in rings with involution

2016 ◽  
Vol 53 (2) ◽  
pp. 138-156
Author(s):  
Dijana Mosić ◽  
Dragan S. Djordjević
Keyword(s):  
Mixed Type ◽  
Reverse Order ◽  
Rings With Involution ◽  
Group Inverses ◽  
Equivalent Conditions

We investigate some equivalent conditions for the reverse order laws (ab)# = b†a# and (ab)# = b#a† in rings with involution. Similar results for (ab)# = b#a* and (ab)# = b*a# are presented too.

Mixed-type reverse-order laws for {1,3,4}-generalized inverses over Hilbert spaces

2012 ◽  
Vol 218 (17) ◽  
pp. 8570-8577 ◽  
Author(s):  
Xiaoji Liu ◽  
Shaowu Huang ◽  
Dragana S. Cvetković-Ilić
Keyword(s):  
Hilbert Spaces ◽  
Mixed Type ◽  
Generalized Inverses ◽  
Reverse Order

scholarly journals Mixed-Type Reverse Order Laws for Generalized Inverses over Hilbert Space

2017 ◽  
Vol 08 (05) ◽  
pp. 637-644
Author(s):  
Haiyan Zhang ◽  
Fengling Lu
Keyword(s):  
Hilbert Space ◽  
Mixed Type ◽  
Generalized Inverses ◽  
Reverse Order

scholarly journals The mixed-type reverse order laws for generalized inverses of the product of two matrices

Filomat ◽  
2013 ◽  
Vol 27 (5) ◽  
pp. 937-947
Author(s):  
Zhiping Xiong
Keyword(s):  
Mixed Type ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Generalized Inverses ◽  
Reverse Order ◽  
Matrix Products ◽  
Schur Complements ◽  
Necessary And Sufficient ◽  
The Relationship

The relationship between generalized inverses of AB and the product of generalized inverses of A and B have been studied in this paper. The necessary and sufficient conditions for a number of mixed-type reverse order laws of generalized inverses of two matrix products are derived by using the maximal ranks of the generalized Schur complements.

scholarly journals Mixed-type reverse order law for Moore-Penrose inverse of products of three elements in ring with involution

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 1997-2008 ◽  
Author(s):  
Long Wang ◽  
Shuang Zhang ◽  
Xiao Zhang ◽  
Jian Chen
Keyword(s):  
Mixed Type ◽  
Reverse Order ◽  
Reverse Order Law ◽  
Rings With Involution

In this paper we establish some results concerning the mixed-type reverse order laws for the Moore-Penrose inverse of various products of three elements in rings with involution.

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