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Volume 37, Issue 4
Least Squares Properties of Generalized Inverses

Predrag S. Stanimirović, Mosić Dijana & Yimin Wei

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 = {Predrag S. and Stanimirović and and 18034 and and Predrag S. Stanimirović and Mosić and Dijana and and 18035 and and Mosić Dijana and Yimin and Wei and and 18036 and and Yimin Wei}, 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.

Predrag S. Stanimirović, Dijana Mosić & YiminWei. (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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