Rank/inertia approaches to weighted least-squares solutions of linear matrix equations

2017 ◽  
Vol 315 ◽  
pp. 400-413 ◽  
Author(s):  
Bo Jiang ◽  
Yongge Tian
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Linear Matrix Equations

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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