scholarly journals Minimum norm least-squares solution to general complex coupled linear matrix equations via iteration

Filomat ◽  
2015 ◽  
Vol 29 (6) ◽  
pp. 1389-1407 ◽  
Author(s):  
Davod Salkuyeh ◽  
Beik Ali
Keyword(s):  
Least Squares ◽  
Linear Matrix ◽  
Minimum Norm ◽  
Matrix Equations ◽  
Least Squares Solution ◽  
General Complex ◽  
Linear Matrix Equations

Least squares solution with the minimum-norm to general matrix equations via iteration

2010 ◽  
Vol 215 (10) ◽  
pp. 3547-3562 ◽  
Author(s):  
Zhao-Yan Li ◽  
Yong Wang ◽  
Bin Zhou ◽  
Guang-Ren Duan
Keyword(s):  
Least Squares ◽  
Minimum Norm ◽  
Matrix Equations ◽  
General Matrix ◽  
Least Squares Solution

scholarly journals A generalized inverse for matrices

1955 ◽  
Vol 51 (3) ◽  
pp. 406-413 ◽  
Author(s):  
R. Penrose
Keyword(s):  
Unique Solution ◽  
Spectral Decomposition ◽  
Generalized Inverse ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Singular Matrix ◽  
Rectangular Matrix ◽  
New Type ◽  
Linear Matrix Equations

This paper describes a generalization of the inverse of a non-singular matrix, as the unique solution of a certain set of equations. This generalized inverse exists for any (possibly rectangular) matrix whatsoever with complex elements. It is used here for solving linear matrix equations, and among other applications for finding an expression for the principal idempotent elements of a matrix. Also a new type of spectral decomposition is given.

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