scholarly journals Notes on Re-nnd generalized inverses

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 1121-1125
Author(s):  
Xifu Liu ◽  
Rouyue Fang
Keyword(s):  
Generalized Inverses ◽  
Equivalent Conditions ◽  
Square Matrix

Motivated by a recent paper, in which the authors studied Re-nnd {1,3}-inverse, {1,4}-inverse and {1,3,4}-inverse of a square matrix, in this paper, we establish some equivalent conditions for the existence of Re-nnd {1,2,3}-inverse, {1,2,4}-inverse and {1,3,4}-inverse. Furthermore, some expressions of these generalized inverses are presented.

scholarly journals The absorption laws for the generalized inverses in rings

2015 ◽  
Vol 30 ◽  
pp. 827-842 ◽  
Author(s):  
Hongwei Jin ◽  
Julio Benitez
Keyword(s):  
Generalized Inverses ◽  
Core Inverse ◽  
Equivalent Conditions ◽  
Appl Math

In this paper, it is given equivalent conditions for the absorption laws in terms of the Moore-Penrose, group, core inverse, core inverse dual, {1}, {1,2}, {1,3}, and {1,4} inverses in rings. The results given here extend the results of [X. Liu, H. Jin, and D.S. Cvetkovi´c-Ili´c. The absorption laws for the generalized inverses. Appl. Math. Comp., 219:2053–2059, 2012].

The commuting inverses of a square matrix

1966 ◽  
Vol 62 (4) ◽  
pp. 667-671 ◽  
Author(s):  
M. J. Englefield
Keyword(s):  
Generalized Inverse ◽  
Linear Equations ◽  
Generalized Inverses ◽  
Arbitrary Matrix ◽  
Square Matrix

An inverse AI for an arbitrary matrix A was first given by Moore (4). Since the application to solution of linear equations only depended on the property A AI A = A, Bjerhammar (2) used this equation to define the set of generalized inverses AI. If A is regular, then only the regular inverse A−1 satisfies this definition. If A is a generalized inverse of AI, so that AI = AI AAI, then AI is a reciprocal inverse.

scholarly journals New characterizations of k-normal and k-EP matrices

2021 ◽  
Author(s):  
ZhiMei Fu ◽  
◽  
KeZheng Zuo ◽  
Yang Chen ◽  
◽  
...  
Keyword(s):  
Generalized Inverses ◽  
The Core ◽  
Equivalent Conditions

In this paper, some new characterizations of k-normal and k-EP matrices are obtained using the core-EP decomposition. We obtain several equivalent conditions for a matrix A to be k-normal and k-EP in terms of certain generalized inverses.

Stochastic local operations and classical communication invariants via square matrix

Laser Physics ◽  
2019 ◽  
Vol 29 (2) ◽  
pp. 025203 ◽  
Author(s):  
Xinwei Zha ◽  
Irfan Ahmed ◽  
Da Zhang ◽  
Wen Feng ◽  
Yanpeng Zhang
Keyword(s):  
Classical Communication ◽  
Square Matrix

scholarly journals Affine Subspaces of Curvature Functions from Closed Planar Curves

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Leonardo Alese
Keyword(s):  
Arc Length ◽  
Planar Curves ◽  
Affine Subspaces ◽  
Planar Curve ◽  
Real Functions ◽  
Discrete Counterpart ◽  
Equivalent Conditions

AbstractGiven a pair of real functions (k, f), we study the conditions they must satisfy for $$k+\lambda f$$ k + λ f to be the curvature in the arc-length of a closed planar curve for all real $$\lambda $$ λ . Several equivalent conditions are pointed out, certain periodic behaviours are shown as essential and a family of such pairs is explicitely constructed. The discrete counterpart of the problem is also studied.

scholarly journals Quasi-ideal Ehresmann transversals: The spined product structure

2021 ◽  
Vol 19 (1) ◽  
pp. 77-86
Author(s):  
Xiangjun Kong ◽  
Pei Wang ◽  
Jian Tang
Keyword(s):  
Structure Theorem ◽  
Product Structure ◽  
Abundant Semigroup ◽  
Spined Product ◽  
Equivalent Conditions

Abstract In any U-abundant semigroup with an Ehresmann transversal, two significant components R and L are introduced in this paper and described by Green’s ∼ \sim -relations. Some interesting properties associated with R and L are explored and some equivalent conditions for the Ehresmann transversal to be a quasi-ideal are acquired. Finally, a spined product structure theorem is established for a U-abundant semigroup with a quasi-ideal Ehresmann transversal by means of R and L.

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