International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1276 2020 2020 University of Wasit, College of Education for Pure Sciences, Mathematics department, Wasit, Iraq S. Obaid Jameel Wasit University, College of Administration and Economics, Statistics Department, Wasit, Iraq A. Mahdi Salih Al-Nahrain University, Department of Information and Communication Engineering, Baghdad, Iraq R. Adnan Jaleel Unvirsity of Babylon, Department of Electrical Engineering, Babylon, Iraq Musaddak M. A. Zahra This paper is dedicated to studying the neutrosophic formula of some famous matrix equations used in theoretical data mining algorithms and control systems by using neutrosophic matrices and refined neutrosophic matrices over neutrosophic real fields. On the other hand, we concentrate on the neutrosophic formula of the Sylvester equation, and Lyapunov equation, where we study their formulas and properties in terms of theorems in the neutrosophic real number field and refined real number field. Also, we illustrate many different examples to clarify the validity of our work. 2022 2022 267 271 10.54216/IJNS.190122 https://www.americaspg.com/articleinfo/21/show/1276