Geodesic
The symmetric minimal rank solution of the matrix equation $AX=B$ and the optimal approximation
The electronic journal of linear algebra, Tome 18 (2009), pp. 264-271.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: By applying the matrix rank method, the set of symmetric matrix solutions with prescribed rank to the matrix equation AX = B is found. An expression is provided for the optimal approximation to the set of the minimal rank solutions.
Classification : 65F15, 65F20
Keywords: symmetric matrix, matrix equation, maximal rank, minimal rank, fixed rank solutions, optimal approximate solution 
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     author = {Xiao, Qing-Feng and Hu, Xi-Yan and Zhang, Lei},
     title = {The symmetric minimal rank solution of the matrix equation $AX=B$ and the optimal approximation},
     journal = {The electronic journal of linear algebra},
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Xiao, Qing-Feng; Hu, Xi-Yan; Zhang, Lei. The symmetric minimal rank solution of the matrix equation $AX=B$ and the optimal approximation. The electronic journal of linear algebra, Tome 18 (2009), pp. 264-271. http://geodesic.mathdoc.fr/item/ELA_2009__18__a35/