Results 1 to 10 of about 59,362 (243)

Reverse Order Law for the Core Inverse in Rings [PDF]

Mediterranean Journal of Mathematics, 2018
In this paper, necessary and sufficient conditions of the onesided reverse order law (ab)((sic)) = b((sic))a((sic)) , the two-sided reverse order law (ab)((sic)) = b((sic))a((sic)) and (ba)((sic)) = a((sic))b((sic)) for the core inverse are given in ...
Patrício, Pedro, Chen, Jianlong, Jianlong Chen, Honglin Zou, Pedro Patrício, Zou, Honglin   +5 more
core   +5 more sources

Reverse order law for the Moore–Penrose inverse

Journal of Mathematical Analysis and Applications, 2010
In this paper we present new results related to the reverse order law for the Moore–Penrose inverse of operators on Hilbert spaces.
Djordjević, Dragan S., Dinčić, Nebojša Č.   +1 more
core   +4 more sources

Reverse Order Law for the Group Inverse in Semigroups and Rings

Communications in Algebra, 2015
International audienceIn this paper, we provide equivalent conditions for the two-sided reverse order law for the group inverse $(ab)^{\sharp}$ = b^{\sharp} a^{\sharp}$ and $(ba)^{\sharp} = a^{\sharp} b^{\sharp}$, in semigroups and rings. Moreover, we
X. Mary, Mary, Xavier
core   +3 more sources

Reverse order law and forward order law for the (b, c)-inverse

The Electronic Journal of Linear Algebra, 2023
The reverse order law and the forward order law have been studied for various types of generalized inverses. The $(b,c)$-inverse is a generalization of some well known generalized inverses, such as the Moore-Penrose inverse, the Drazin inverse, the core ...
Ivana Stanisev, Ke, Yuanyuan, Jelena Visnjic, Stanisev, Ivana, Visnjic, Jelena, Yuanyuan Ke   +5 more
core   +2 more sources

The reverse order law revisited

Linear Algebra and its Applications, 1986
Necessary and sufficient conditions are given for the triple reverse order law (ABC)† = C†B†A† to hold.
Hartwig, R.E.
core   +3 more sources

The reverse order law (AB)− = B−A−

Linear Algebra and its Applications, 1974
Some new results on “reverse order law” related to the generalized inverse of the product of two matrices are obtained, and Greville's and others' previous results are extended.
Shinozaki, Nobuo, Sibuya, Masaaki
core   +3 more sources

Reverse order law for the group inverses

Journal of Mathematical Analysis and Applications, 2011
This paper is to present some equivalent conditions concerning the reverse order law (AB)#=B#A# for the group invertible operators A, B on a Hilbert space ...
Deng, Chun Yuan, Chun Yuan Deng
core   +2 more sources

Some results on matrix partial orderings and reverse order law

The Electronic Journal of Linear Algebra, 2010
Some results relating different matrix partial orderings and the reverse order law for the Moore-Penrose inverse and the group inverse are given.
Benitez, Julio, Liu, Xiaoji, Zhong, Jin
core   +3 more sources

Further results on the reverse order law for the group inverse in rings [PDF]

Applied Mathematics and Computation, 2014
In this paper, we use the Drazin inverse to derive some new equivalences of the reverse order law for the group inverse in unitary rings. Moreover, if the ring has an involution, we present more equivalences when both involved elements are EP.
Zhang, Miao, Benítez López, Julio, Liu, Xiaoji   +2 more
core   +3 more sources

Mixed-type reverse order law of (AB)(13)

Linear Algebra and its Applications, 2009
Some mixed-type reverse-order laws of (AB)† have been proposed and studied by Tian. In this paper, by applying the extremal rank relations of generalized Schur complements and the P-SVD of two matrices A and B, we study two kind of mixed-type reverse ...
Wang, Minghui, Wei, Musheng, Jia, Zhigang   +2 more
core   +2 more sources