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.

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].

scholarly journals Rank Equalities Related to the Generalized Inverses A‖(B1,C1), D‖(B2,C2) of Two Matrices A and D

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 539 ◽  
Author(s):  
Wenjie Wang ◽  
Sanzhang Xu ◽  
Julio Benítez
Keyword(s):  
Generalized Inverses ◽  
Drazin Inverse ◽  
Group Inverse ◽  
Complex Matrix ◽  
The Core ◽  
Core Inverse

Let A be an n × n complex matrix. The ( B , C ) -inverse A ∥ ( B , C ) of A was introduced by Drazin in 2012. For given matrices A and B, several rank equalities related to A ∥ ( B 1 , C 1 ) and B ∥ ( B 2 , C 2 ) of A and B are presented. As applications, several rank equalities related to the inverse along an element, the Moore-Penrose inverse, the Drazin inverse, the group inverse and the core inverse are obtained.

scholarly journals Rank equalities related to a class of outer generalized inverse

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5611-5622 ◽  
Author(s):  
Jianlong Chen ◽  
Sanzhang Xu ◽  
Julio Benítez ◽  
Xiaofeng Chen
Keyword(s):  
Generalized Inverse ◽  
Drazin Inverse ◽  
The Core ◽  
Core Inverse ◽  
Equivalent Conditions

In 2012, Drazin introduced a class of outer generalized inverse in a ring R, the (b,c)-inverse of a for a, b, c ? R and denoted by a||(b,c). In this paper, rank equalities of AkA||(B,C)- A||(B,C)Ak and (A*)kA||(B,C)- A||(B,C)(A*)k are obtained. As applications, weinvestigate equivalent conditions for the equalities (A*)kA||(B,C) = A||(B,C)(A*)k and AkA||(B,C) = A||(B,C)Ak. As corollaries we obtain rank equalities related to the Moore-Penrose inverse, the core inverse, and the Drazin inverse. The paper finishes with some rank equalities involving different e

scholarly journals The pseudo core inverse of a companion matrix

2018 ◽  
Vol 55 (3) ◽  
pp. 407-420
Author(s):  
Yuefeng Gao ◽  
Jianlong Chen ◽  
Pedro Patrício ◽  
Dingguo Wang
Keyword(s):  
Toeplitz Matrix ◽  
Toeplitz Matrices ◽  
Generalized Inverses ◽  
Companion Matrix ◽  
Complex Matrix ◽  
Complex Matrices ◽  
The Core ◽  
Core Inverse ◽  
Companion Matrices ◽  
Existence Criteria

The notion of core inverse was introduced by Baksalary and Trenkler for a complex matrix of index 1. Recently, the notion of pseudo core inverse extended the notion of core inverse to an element of an arbitrary index in *-rings; meanwhile, it characterized the core-EP inverse introduced by Manjunatha Prasad and Mohana for complex matrices, in terms of three equations. Many works have been done on classical generalized inverses of companion matrices and Toeplitz matrices. In this paper, we discuss existence criteria and formulae of the pseudo core inverse of a companion matrix over a *-ring. A {1,3}-inverse of a Toeplitz matrix plays an important role in that process.

scholarly journals Further characterizations of the weak core inverse of matrices and the weak core matrix

2021 ◽  
Vol 7 (3) ◽  
pp. 3630-3647
Author(s):  
Zhimei Fu ◽  
◽  
Kezheng Zuo ◽  
Yang Chen
Keyword(s):  
Null Space ◽  
Matrix Equations ◽  
Range Space ◽  
The Core ◽  
Core Inverse ◽  
Core Matrix ◽  
Equivalent Conditions

<abstract><p>The present paper is devoted to characterizing the weak core inverse and the weak core matrix using the core-EP decomposition. Some new characterizations of the weak core inverse are presented by using its range space, null space and matrix equations. Additionally, we give several new representations and properties of the weak core inverse. Finally, we consider several equivalent conditions for a matrix to be a weak core matrix.</p></abstract>

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.

What face familiarity feelings say about the lateralization of specific entities within the core system

2019 ◽  
Vol 42 ◽  
Author(s):  
Guido Gainotti
Keyword(s):  
Temporal Lobe ◽  
Memory System ◽  
Core System ◽  
The Core ◽  
Memory Traces ◽  
Specific Memory ◽  
Target Article ◽  
Temporal Structures ◽  
The Right

Abstract The target article carefully describes the memory system, centered on the temporal lobe that builds specific memory traces. It does not, however, mention the laterality effects that exist within this system. This commentary briefly surveys evidence showing that clear asymmetries exist within the temporal lobe structures subserving the core system and that the right temporal structures mainly underpin face familiarity feelings.

A scanning electron microscopic study on dissolving process of cholesterol gallstones by chenodeoxycholic acid (CDCA)

1978 ◽  
Vol 36 (2) ◽  
pp. 522-523
Author(s):  
T. Kanetaka ◽  
M. Cho ◽  
S. Kawamura ◽  
T. Sado ◽  
K. Hara
Keyword(s):  
Electron Microscope ◽  
Chenodeoxycholic Acid ◽  
Outer Surface ◽  
Electron Microscopic ◽  
Cholesterol Gallstones ◽  
The Core ◽  
Scanning Electron Microscopic Study ◽  
Scanning Electron Microscopic ◽  
Acceleration Voltage ◽  
Scanning Electron

The authors have investigated the dissolution process of human cholesterol gallstones using a scanning electron microscope(SEM). This study was carried out by comparing control gallstones incubated in beagle bile with gallstones obtained from patients who were treated with chenodeoxycholic acid(CDCA).The cholesterol gallstones for this study were obtained from 14 patients. Three control patients were treated without CDCA and eleven patients were treated with CDCA 300-600 mg/day for periods ranging from four to twenty five months. It was confirmed through chemical analysis that these gallstones contained more than 80% cholesterol in both the outer surface and the core.The specimen were obtained from the outer surface and the core of the gallstones. Each specimen was attached to alminum sheet and coated with carbon to 100Å thickness. The SEM observation was made by Hitachi S-550 with 20 kV acceleration voltage and with 60-20, 000X magnification.

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