Generalized Product of Two Square Matrices and Application for Some Algebraic Equations
In this paper, a generalized matrix product is introduced and related properties are studied as well. Afterwards, we show how our approach can be applied to the so-called Sylvester and Lyaponov matrix equations for obtaining their related solutions in terms of the generalized matrix product. Numerical examples illustrating the theoretical study are also discussed.
KeywordsSquare matrix Generalized matrix product Matrix-convexity Matrix equations Sylvester equation Lyapunov equation
Mathematics Subject Classification15A60 15A24 26A51 47A64
- 9.Lefschetz, S., Lasalle, J.P.: Stability by Lyapunov direct method. Academic Press, New York (1987)Google Scholar