scholarly journals Erratum and Addendum: Positive Semidefinite Matrices: Characterization via Conical Hulls and Least-Squares Solution of a Matrix Equation

1990 ◽  
Vol 28 (1) ◽  
pp. 250-251 ◽  
Author(s):  
J. C. Allwright ◽  
K. C. Woodgate
Keyword(s):  
Least Squares ◽  
Matrix Equation ◽  
Positive Semidefinite ◽  
Positive Semidefinite Matrices ◽  
Least Squares Solution

scholarly journals On the general strong fuzzy solutions of general fuzzy matrix equation involving the Core-EP inverse

2021 ◽  
Vol 7 (2) ◽  
pp. 3221-3238
Author(s):  
Hongjie Jiang ◽  
◽  
Xiaoji Liu ◽  
Caijing Jiang
Keyword(s):  
Least Squares ◽  
Unique Solution ◽  
Matrix Equation ◽  
Fuzzy Matrix ◽  
Least Squares Solution ◽  
The Core ◽  
Fuzzy Solutions

<abstract><p>The inconsistent or consistent general fuzzy matrix equation are studied in this paper. The aim of this paper is threefold. Firstly, general strong fuzzy matrix solutions of consistent general fuzzy matrix equation are derived, and an algorithm for obtaining general strong fuzzy solutions of general fuzzy matrix equation by Core-EP inverse is also established. Secondly, if inconsistent or consistent general fuzzy matrix equation satisfies $ X\in R(S^{k}) $, the unique solution or unique least squares solution of consistent or inconsistent general fuzzy matrix equation are given by Core-EP inverse. Thirdly, we present an algorithm for obtaining Core-EP inverse. Finally, we present some examples to illustrate the main results.</p></abstract>

scholarly journals Minimal properties of the Drazin-inverse solution of a matrix equation

Filomat ◽  
2014 ◽  
Vol 28 (2) ◽  
pp. 383-395
Author(s):  
Marko Miladinovic ◽  
Sladjana Miljkovic ◽  
Predrag Stanimirovic
Keyword(s):  
Least Squares ◽  
Minimization Problem ◽  
Matrix Equation ◽  
Inverse Solution ◽  
Drazin Inverse ◽  
Minimal Norm ◽  
Least Squares Solution ◽  
The Matrix

We present the Drazin-inverse solution of the matrix equation AXB = G as a least-squares solution of a specified minimization problem. Some important properties of the Moore-Penrose inverse are extended on the Drazin inverse by exploring the minimal norm properties of the Drazin-inverse solution of the matrix equation AXB = G. The least squares properties of the Drazin-inverse solution lead to new representations of the Drazin inverse of a given matrix, which are justified by illustrative examples.

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