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.

scholarly journals Classification and approximation of solutions to Sylvester matrix equation

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4261-4280 ◽  
Author(s):  
Bogdan Djordjevic ◽  
Nebojsa Dincic
Keyword(s):  
Least Squares ◽  
Matrix Equation ◽  
Infinitely Many Solutions ◽  
Sylvester Matrix Equation ◽  
Minimal Norm ◽  
Sylvester Matrix

In this paperwesolve Sylvester matrix equation with infinitely-many solutions and conduct their classification. If the conditions for their existence are not met, we provide a way for their approximation by least-squares minimal-norm method.

Sign in / Sign up

Export Citation Format

Share Document