After a final discussion of positive definite matrices, we learn about “similar” matrices: B = M−1AM for some invertible matrix M. Square matrices can be grouped by similarity, and each group has a “nicest” representative in Jordan normal form. This form tells at a glance the eigenvalues and the number of eigenvectors.
Lecture Video and Summary
- Watch the video lecture Lecture 28: Similar Matrices and Jordan Form
- Read the accompanying lecture summary (PDF)
- Lecture video transcript (PDF)
- Read Section 6.6 in the 4th edition or Section 6.2 in the 5th edition.
Problem Solving Video
Problems and Solutions
Work the problems on your own and check your answers when you’re done.