On the solving matrix equations by using the spectral representation

محورهای موضوعی : Linear and multilinear algebra; matrix theory

A. M. Nazari ¹ , S. Mollaghasemi ² , F. Bahmani ³

1 - Department of Mathematics, Faculty of Science, Arak university, Arak, PO. Box 38156-8-8349, Iran
2 - Department of Mathematics, Faculty of Science, Arak university, Arak, PO. Box 38156-8-8349, Iran
3 - Department of Mathematics, Faculty of Science, Arak university, Arak, PO. Box 38156-8-8349, Iran

تاریخ دریافت : 1397/03/13 تاریخ پذیرش : 1397/09/19 تاریخ انتشار : 1397/08/10

کلید واژه: Lyapanov equation, square matrix equations, spectral representation,

چکیده مقاله :

‎The purpose of this paper is to solve two types of Lyapunov equations and quadratic matrix equations by using the spectral representation‎. ‎We focus on solving Lyapunov equations $AX+XA^*=C$ and $AX+XA^{T}=-bb^{T}$ for $A‎, ‎X \in \mathbb{C}^{n \times n}$ and $b \in \mathbb{C} ^{n \times s}$ with $s < n$‎, ‎which $X$ is unknown matrix‎. ‎Also‎, ‎we suggest the new method for solving quadratic matrix equations $AX^{2}+BX+C=0$‎, ‎where $A‎, ‎B‎, ‎C‎, ‎X \in \mathbb{C}^{n \times n}$ and $X$ is unknown matrix with similar method‎.

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