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Volume 37, Issue 4
Least Squares Properties of Generalized Inverses

Predrag S. Stanimirović, Mosić Dijana & Yimin Wei

DOI: 10.4208/cmr.2021-0011

Commun. Math. Res., 37 (2021), pp. 421-447.

Published online: 2021-08

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  • Abstract

The aim of this paper is to systematize solutions of some systems of linear equations in terms of generalized inverses. As a significant application of the Moore-Penrose inverse, the best approximation solution to linear matrix equations (i.e. both least squares and the minimal norm) is considered. Also, characterizations of least squares solution and solution of minimum norm are given. Basic properties of the Drazin-inverse solution and the outer-inverse solution are present. Motivated by recent research, important least square properties of composite outer inverses are collected.

  • Keywords

Outer inverse, Moore-Penrose inverse, DMP inverse, core-EP inverse.

  • AMS Subject Headings

15A09, 15A24, 65F05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-37-421, author = {Stanimirović , Predrag S.Dijana , Mosić and Wei , Yimin}, title = {Least Squares Properties of Generalized Inverses}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {37}, number = {4}, pages = {421--447}, abstract = {

The aim of this paper is to systematize solutions of some systems of linear equations in terms of generalized inverses. As a significant application of the Moore-Penrose inverse, the best approximation solution to linear matrix equations (i.e. both least squares and the minimal norm) is considered. Also, characterizations of least squares solution and solution of minimum norm are given. Basic properties of the Drazin-inverse solution and the outer-inverse solution are present. Motivated by recent research, important least square properties of composite outer inverses are collected.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2021-0011}, url = {http://global-sci.org/intro/article_detail/cmr/19437.html} }
TY - JOUR T1 - Least Squares Properties of Generalized Inverses AU - Stanimirović , Predrag S. AU - Dijana , Mosić AU - Wei , Yimin JO - Communications in Mathematical Research VL - 4 SP - 421 EP - 447 PY - 2021 DA - 2021/08 SN - 37 DO - http://doi.org/10.4208/cmr.2021-0011 UR - https://global-sci.org/intro/article_detail/cmr/19437.html KW - Outer inverse, Moore-Penrose inverse, DMP inverse, core-EP inverse. AB -

The aim of this paper is to systematize solutions of some systems of linear equations in terms of generalized inverses. As a significant application of the Moore-Penrose inverse, the best approximation solution to linear matrix equations (i.e. both least squares and the minimal norm) is considered. Also, characterizations of least squares solution and solution of minimum norm are given. Basic properties of the Drazin-inverse solution and the outer-inverse solution are present. Motivated by recent research, important least square properties of composite outer inverses are collected.

Stanimirović , Predrag S.Dijana , Mosić and Wei , Yimin. (2021). Least Squares Properties of Generalized Inverses. Communications in Mathematical Research . 37 (4). 421-447. doi:10.4208/cmr.2021-0011
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