Comptes Rendus
Optimal Control/Numerical Analysis
On solutions of the matrix equations KXEXF=BY and MXF2+DXF+KX=BY
[Sur les solutions des équations matricielles KXEXF=BY et MXF2+DXF+KX=BY]
Comptes Rendus. Mathématique, Volume 350 (2012) no. 19-20, pp. 903-906.

Dans cette note on étudie les solutions des équations généralisées de Sylvester KXEXF=BY et MFX2+DXF+KX=BY, on donne des expressions explicites des solutions de ces équations en utilisant des transformations matricielles et le polynôme minimal de la matrice F.

This note studies the solutions of generalized Sylvester equations KXEXF=BY and MXF2+DXF+KX=BY, and obtains explicit solutions of the equations by using some matrix transformations and the minimal polynomial of the matrix F.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.10.011

Yongxin Yuan 1 ; Jiashang Jiang 1

1 School of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang 212003, PR China
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Yongxin Yuan; Jiashang Jiang. On solutions of the matrix equations $ KX-EXF=BY$ and $ MX{F}^{2}+DXF+KX=BY$. Comptes Rendus. Mathématique, Volume 350 (2012) no. 19-20, pp. 903-906. doi : 10.1016/j.crma.2012.10.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.10.011/

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