Eigenvectors and Their Applications in Linear Systems (Al-Farooq Journal of Sciences, 2026)
This study aims to investigate eigenvalues and eigenvectors as fundamental concepts in linear algebra due to their significant role in analyzing and simplifying linear systems. The research discusses the basic definitions of these concepts and the methods used to compute them through the characteristic equation. It also explains their relationship with linear transformations and matrices. Furthermore, the study highlights their importance in transforming matrices into diagonal form, which simplifies solving linear systems and differential equations. Practical applications of eigenvalues and eigenvectors in various fields such as engineering, physics, and computer science are also presented. The study concludes that a proper understanding of these concepts greatly contributes to simplifying mathematical models and efficiently analyzing complex systems.
Keywords: Eigenvalues- Eigenvectors- Linear Transformations- Characteristic Equation Linear Systems Analysis.