Lecture 9: Eigenvalues & Eigenvectors in Linear Algebra (AAS103)

**Introduction** This video is Lecture 9 of the Linear Algebra course for engineering programs at Dr. A.P.J. Abdul Kalam Technical University (AKTU) in India, providing a systematic exposition of eigenvalues and eigenvectors — a core concept in linear algebra. This topic not only serves as an essential foundation for subsequent subjects such as matrix diagonalization and solving differential equations, but also has direct applications in engineering fields including structural mechanics and vibration modal analysis. **Key Highlights:** The course begins with fundamental definitions, progressively derives the method for solving the characteristic equation, and walks through representative worked examples demonstrating how to compute eigenvalues and their corresponding eigenvectors. The logic is clear and the steps are complete, helping learners build a solid problem-solving framework. **Target Audience:** Undergraduate students in science and engineering (especially civil, mechanical, and related disciplines), candidates preparing for postgraduate entrance exams, and self-learners looking to refresh their linear algebra fundamentals. **Runtime:** Approximately 50 minutes. It is recommended to watch in stages while taking notes, prioritizing the step-by-step solution processes in the worked examples.