If the product Ax points in the same direction as the vector x, we say that x is an eigenvector of A. Eigenvalues and eigenvectors describe what happens when a matrix is multiplied by a vector. In this session we learn how to find the eigenvalues and eigenvectors of a matrix.
Lecture Video and Summary
- Watch the video lecture
Eigenvalues and Eigenvectors (00:51:23)
Lecture 21: Eigenvalues and Eigenvectors
- Read the accompanying lecture summary (PDF)
- Lecture video transcript (PDF)
- Read Section 6.1 through 6.2 in the 4th or 5th edition.
Problem Solving Video
- Watch the recitation video on
Eigenvalues and Eigenvectors (00:09:21)
Problem Solving: Eigenvalues and Eigenvectors
- Recitation video transcript (PDF)
Problems and Solutions
Work the problems on your own and check your answers when you're done.
These demonstrations employ Java® applets with voice-over narration by Professor Strang.
Mini-lectures on Eigenvalues
These mini-lectures with voice-over narration below help to explain some key Eigenvalue concepts.
- Eigenvectors and Trace
- Differential Equations
- Positive Definite
*Funding for these demonstrations was provided by a grant from the The d'Arbeloff Fund for Excellence in MIT Education as part of The d'Arbeloff Interactive Mathematics Project (d'A I M P).