If A has n independent eigenvectors, we can write A = SΛS−1, where Λ is a diagonal matrix containing the eigenvalues of A. This allows us to easily compute powers of A which in turn allows us to solve difference equations uk+1 = Auk.
Lecture Video and Summary
- Watch the video lecture Diagonalization and Powers of A (00:51:50)
Lecture 22: Diagonalization and Powers of A
- Read the accompanying lecture summary (PDF)
- Lecture video transcript (PDF)
- Read Section 6.2 in the 4th or 5th edition.
Problem Solving Video
- Watch the recitation video on Powers of a Matrix (00:09:06)
Problem Solving: Powers of a Matrix
- Recitation video transcript (PDF)
Problems and Solutions
Work the problems on your own and check your answers when you're done.