On solutions of the matrix equations $ KX-EXF=BY$ and $ MX{F}^{2}+DXF+KX=BY$

Yuan, Yongxin; Jiang, Jiashang

doi:10.1016/j.crma.2012.10.011

Optimal Control/Numerical Analysis

On solutions of the matrix equations

K X - E X F = B Y

and

M X F^{2} + D X F + K X = B Y

[Sur les solutions des équations matricielles

K X - E X F = B Y

M X F^{2} + D X F + K X = B Y

]

Présenté par : Olivier Pironneau

Yuan, Yongxin ¹ ; Jiang, Jiashang ¹

¹ School of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang 212003, PR China

Comptes Rendus. Mathématique, Tome 350 (2012) no. 19-20, pp. 903-906.

Résumé
Abstract

Dans cette note on étudie les solutions des équations généralisées de Sylvester $K X - E X F = B Y$ et $M F X^{2} + D X F + K X = B Y$ , 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 $K X - E X F = B Y$ and $M X F^{2} + D X F + K X = B Y$ , and obtains explicit solutions of the equations by using some matrix transformations and the minimal polynomial of the matrix F.

Reçu le : 2012-05-16
Accepté le : 2012-10-09
Publié le : 2012-10-01

DOI : 10.1016/j.crma.2012.10.011

Affiliations des auteurs :

Yuan, Yongxin ¹ ; Jiang, Jiashang ¹

¹ School of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang 212003, PR China

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     title = {On solutions of the matrix equations $ KX-EXF=BY$ and $ MX{F}^{2}+DXF+KX=BY$},
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Yuan, Yongxin; Jiang, Jiashang. On solutions of the matrix equations $ KX-EXF=BY$ and $ MX{F}^{2}+DXF+KX=BY$. Comptes Rendus. Mathématique, Tome 350 (2012) no. 19-20, pp. 903-906. doi : 10.1016/j.crma.2012.10.011. http://www.numdam.org/articles/10.1016/j.crma.2012.10.011/

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