scholarly journals Perturbation theory for core and core-EP inverses of tensor via Einstein product

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5207-5217 ◽  
Author(s):  
Hong-Mei Du ◽  
Bing-Xue Wang ◽  
Hai-Feng Ma
Keyword(s):  
Perturbation Theory ◽  
Perturbation Bounds ◽  
The Core ◽  
Core Inverse ◽  
Einstein Product

In this paper, for given tensors A,? and B = A+E, we investigate the perturbation bounds for the core inverse A# and core-EP inverse A+ under some conditions via Einstein product.

scholarly journals The core inverse and constrained matrix approximation problem

2020 ◽  
Vol 18 (1) ◽  
pp. 653-661 ◽  
Author(s):  
Hongxing Wang ◽  
Xiaoyan Zhang
Keyword(s):  
Unique Solution ◽  
Approximation Problem ◽  
Frobenius Norm ◽  
Matrix Approximation ◽  
The Core ◽  
Core Inverse

Abstract In this article, we study the constrained matrix approximation problem in the Frobenius norm by using the core inverse: ||Mx-b|{|}_{F}=\hspace{.25em}\min \hspace{1em}\text{subject}\hspace{.25em}\text{to}\hspace{1em}x\in {\mathcal R} (M), where M\in {{\mathbb{C}}}_{n}^{\text{CM}} . We get the unique solution to the problem, provide two Cramer’s rules for the unique solution and establish two new expressions for the core inverse.

scholarly journals O2 State in 18 O by using Core – Polarization effects

2008 ◽  
pp. 66-72
Keyword(s):  
Perturbation Theory ◽  
Experimental Studies ◽  
Form Factors ◽  
Wave Model ◽  
Collective Model ◽  
Core Polarization ◽  
Polarization Effects ◽  
The Core ◽  
The Subject ◽  
Space Wave

Coulomb form factors for E0 transition in 18O are discussed taking into account core-polarization effects. These effects are taken into account through the collective model of Tassie and also through a microscopic perturbation theory including excitations up to 2p1f shell. Space wave model functions defined for the orbits 1 and 2125O nucleus has been the subject of extensive theoretical and experimental studies, which received much attention in last decade [Alex Brown et.al.2005]. The 18O system contains two neutrons in addition to the16O core distributed in the sd – shell. d1 are obtained from the diagonalization of the interaction Hamilonian of Wildenthal. The calculations include the 0 2state with excitation energies3.6337MeV. The core – polarization effects which incorporate the ollective model of Tassei describe the data very well for this state.

scholarly journals Determinantal Representations of the Core Inverse and Its Generalizations with Applications

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Ivan I. Kyrchei
Keyword(s):  
Direct Method ◽  
Linear Equations ◽  
Close Relation ◽  
Numerical Example ◽  
Determinantal Representation ◽  
The Core ◽  
Core Inverse ◽  
Cramer’S Rule ◽  
The Right

In this paper, we give the direct method to find of the core inverse and its generalizations that is based on their determinantal representations. New determinantal representations of the right and left core inverses, the right and left core-EP inverses, and the DMP, MPD, and CMP inverses are derived by using determinantal representations of the Moore-Penrose and Drazin inverses previously obtained by the author. Since the Bott-Duffin inverse has close relation with the core inverse, we give its determinantal representation and its application in finding solutions of the constrained linear equations that is an analog of Cramer’s rule. A numerical example to illustrate the main result is given.

Perturbation theory for Moore–Penrose inverse of tensor via Einstein product

2019 ◽  
Vol 38 (3) ◽  
Author(s):  
Haifeng Ma ◽  
Na Li ◽  
Predrag S. Stanimirović ◽  
Vasilios N. Katsikis
Keyword(s):  
Perturbation Theory ◽  
Einstein Product

Perturbation bounds for the W-weighted core-EP inverse

2019 ◽  
Vol 19 (12) ◽  
pp. 2050232
Author(s):  
Yuefeng Gao
Keyword(s):  
Integral Representation ◽  
Rectangular Matrix ◽  
Perturbation Bounds ◽  
The Core ◽  
Special Case ◽  
Stable Matrix

In this paper, perturbation bounds are provided for the [Formula: see text]-weighted core-EP inverse of a rectangular matrix under reasonable conditions. Perturbation bounds for the core-EP inverse could be stated as a special case. Then, the continuity of the [Formula: see text]-weighted core-EP inverse is considered from the perspective of equations. Finally, we give an application to a semi-stable matrix involving an integral representation of the [Formula: see text]-weighted core-EP inverse of a perturbed matrix.

Revisitation of the core inverse

2015 ◽  
Vol 20 (5) ◽  
pp. 381-385 ◽  
Author(s):  
Gaojun Luo ◽  
Kezheng Zuo ◽  
Liang Zhou
Keyword(s):  
The Core ◽  
Core Inverse
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