Studying Some Classical Matrix Equations over the Real Numbers Field | ||
| البحوث التطبيقية في العلوم والانسانيات | ||
| Volume 2, Issue 1, 2025, Pages 106-121 PDF (955.56 K) | ||
| Document Type: المقالة الأصلية | ||
| DOI: 10.21608/aash.2025.454152 | ||
| Authors | ||
| Salma Sobhy; Ohoud Essam Alden; Mahitab Amal; Marzouka Mohamed; Mariam Robell; Mariam Mostafa; Mahmoud Saad Mehany | ||
| Assistant Professor of Pure and Computational Mathematics, Mathematics Department, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt . | ||
| Abstract | ||
| 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. | ||
| Keywords | ||
| Matrix Inverse; Left and Right Inverses; Moore-Penrose Inverse; Full Rank Matrices; Linear Equation Solution | ||
|
Statistics Article View: 36 PDF Download: 19 |
||
