Complex Analysis and Operator Theory

, Volume 12, Issue 4, pp 969–986 | Cite as

Generalized Product of Two Square Matrices and Application for Some Algebraic Equations

  • Mustapha Raïssouli
  • Ibrahim Al-Subaihi


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.


Square matrix Generalized matrix product Matrix-convexity Matrix equations Sylvester equation Lyapunov equation 

Mathematics Subject Classification

15A60 15A24 26A51 47A64 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceTaibah UniversityAl Madinah Al MunawwarahKingdom of Saudi Arabia
  2. 2.Science Faculty, Department of MathematicsMoulay Ismail UniversityMeknesMorocco

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