Fast enclosure for the minimum norm least squares solution of the matrix equation A X B = C

2015 ◽  
Vol 22 (3) ◽  
pp. 548-563
Author(s):  
Shinya Miyajima
Keyword(s):  
Least Squares ◽  
Matrix Equation ◽  
Minimum Norm ◽  
Least Squares Solution ◽  
The Matrix

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.

Sign in / Sign up

Export Citation Format

Share Document