Geodesic
Solution of linear matrix equations in a *congruence class
The electronic journal of linear algebra, Tome 13 (2005), pp. 153-156.

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

Summary: The possible *congruence classes of a square solution to the real or complex linear matrix equation AX = B are determined. The solution is elementary and self contained, and includes several known results as special cases, e.g., X is Hermitian or positive semidefinite, and X is real with positive definite symmetric part.
Classification : 15A04, 15A06, 15A21, 15A57, 15A63
Keywords: linear matrix equations, *Congruence, positive definite matrix, positive semidefinite matrix, Hermitian part, symmetric part 
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     author = {Horn, Roger A. and Sergeichuk, Vladimir V. and Shaked-Monderer, Naomi},
     title = {Solution of linear matrix equations in a *congruence class},
     journal = {The electronic journal of linear algebra},
     pages = {153--156},
     publisher = {mathdoc},
     volume = {13},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2005__13__a14/}
}
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Horn, Roger A.; Sergeichuk, Vladimir V.; Shaked-Monderer, Naomi. Solution of linear matrix equations in a *congruence class. The electronic journal of linear algebra, Tome 13 (2005), pp. 153-156. http://geodesic.mathdoc.fr/item/ELA_2005__13__a14/