Group inverse for a class of centrosymmetric matrix

2018 ◽  
Vol 13 (8) ◽  
pp. 351-356
Author(s):  
Mei Wang ◽  
Junqing Wang
Keyword(s):  
Group Inverse ◽  
Centrosymmetric Matrix

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

Group inverse sampling: An economical approach to inverse sampling

2017 ◽  
Vol 28 (7) ◽  
pp. e2459 ◽  
Author(s):  
Bardia Panahbehagh ◽  
David R. Smith
Keyword(s):  
Group Inverse ◽  
Inverse Sampling

scholarly journals Group inverse matrix of the normalized Laplacian on subdivision networks

2020 ◽  
pp. 23-23
Author(s):  
Ángeles Carmona ◽  
Margarida Mitjana ◽  
Enric Monsó
Keyword(s):  
Inverse Matrix ◽  
Group Inverse ◽  
Kirchhoff Index ◽  
Base Network

In this paper we consider a subdivision of a given network and we show how the group inverse matrix of the normalized laplacian of the subdivision network is related to the group inverse matrix of the normalized laplacian of the initial given network. Our approach establishes a relationship between solutions of related Poisson problems on both structures and takes advantage on the properties of the group inverse matrix. As a consequence we get formulae for effective resistances and the Kirchhoff Index of the subdivision network expressed in terms of its corresponding in the base network. Finally, we study two examples where the base network are the star and the wheel, respectively.

The Word Problem for Orthogroups

1981 ◽  
Vol 33 (4) ◽  
pp. 893-900 ◽  
Author(s):  
J. A. Gerhard ◽  
Mario Petrich
Keyword(s):  
Regular Semigroup ◽  
Maximal Subgroup ◽  
Word Problem ◽  
Unary Operation ◽  
Group Inverse ◽  
Completely Regular Semigroup ◽  
Completely Regular ◽  
Image Position ◽  
Natural Way

A semigroup which is a union of groups is said to be completely regular. If in addition the idempotents form a subsemigroup, the semigroup is said to be orthodox and is called an orthogroup. A completely regular semigroup S is provided in a natural way with a unary operation of inverse by letting a-l for a ∈ S be the group inverse of a in the maximal subgroup of S to which a belongs. This unary operation satisfies the identities(1)(2)(3)In fact a completely regular semigroup can be defined as a unary semigroup (a semigroup with an added unary operation) satisfying these identities. An orthogroup can be characterized as a completely regular semigroup satisfying the additional identity(4)

Explicit group inverse of an innovative patterned matrix

2016 ◽  
Vol 274 ◽  
pp. 220-228 ◽  
Author(s):  
Zhao-lin Jiang ◽  
Dan-dan Wang
Keyword(s):  
Group Inverse

scholarly journals The pseudoinverse of a centrosymmetric matrix

1973 ◽  
Vol 6 ◽  
pp. 201-204 ◽  
Author(s):  
W.C. Pye ◽  
T.L. Boullion ◽  
T.A. Atchison
Keyword(s):  
Centrosymmetric Matrix

Weak group inverses in proper ∗-rings

2019 ◽  
Vol 19 (12) ◽  
pp. 2050238 ◽  
Author(s):  
Mengmeng Zhou ◽  
Jianlong Chen ◽  
Yukun Zhou
Keyword(s):  
Group Inverse ◽  
Complex Matrices ◽  
Weak Group ◽  
Group Inverses

In proper ∗-rings, we characterize weak group inverses by three equations. It generalizes the notion of weak group inverse, which was introduced by Wang and Chen for complex matrices in 2018. Some new equivalent characterizations for elements to be weak group invertible are presented. Furthermore, we define the group-EP decomposition. Some properties of the weak group inverse are established by the group-EP decomposition.

Sign in / Sign up

Export Citation Format

Share Document