Matrices are fundamental tools in linear algebra, widely used in various mathematical, engineering, and physical applications. In this paper, we give a review of the sufficient and necessary conditions for three classical matrix equations: AX = B, XB = C, and AXB = C. We also discuss the general solution using the Moore-Penrose inverse and provide illustrative examples. Additionally, we explore the concepts of the left and right inverse, their existence conditions, and their role in solving linear equations. Furthermore, we present a proof of existence and uniqueness of these inverses, ensuring well-defined solutions. This study establishes a solid theoretical foundation for understanding and computing matrix inverses in linear algebra.
Sobhy, Salma, Alden, Ohoud Essam, Amal, Mahitab, Mohamed, Marzouka, Robell, Mariam, Mostafa, Mariam, & Mehany, Mahmoud Saad. (2025). Studying Some Classical Matrix Equations over the Real Numbers Field. البحوث التطبيقية في العلوم والانسانيات, 2(1), 106-121. doi: 10.21608/aash.2025.454152
MLA
Salma Sobhy; Ohoud Essam Alden; Mahitab Amal; Marzouka Mohamed; Mariam Robell; Mariam Mostafa; Mahmoud Saad Mehany. "Studying Some Classical Matrix Equations over the Real Numbers Field", البحوث التطبيقية في العلوم والانسانيات, 2, 1, 2025, 106-121. doi: 10.21608/aash.2025.454152
HARVARD
Sobhy, Salma, Alden, Ohoud Essam, Amal, Mahitab, Mohamed, Marzouka, Robell, Mariam, Mostafa, Mariam, Mehany, Mahmoud Saad. (2025). 'Studying Some Classical Matrix Equations over the Real Numbers Field', البحوث التطبيقية في العلوم والانسانيات, 2(1), pp. 106-121. doi: 10.21608/aash.2025.454152
VANCOUVER
Sobhy, Salma, Alden, Ohoud Essam, Amal, Mahitab, Mohamed, Marzouka, Robell, Mariam, Mostafa, Mariam, Mehany, Mahmoud Saad. Studying Some Classical Matrix Equations over the Real Numbers Field. البحوث التطبيقية في العلوم والانسانيات, 2025; 2(1): 106-121. doi: 10.21608/aash.2025.454152
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