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 Similar Matrices and Jordan Form (00:45:56)
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
- Watch the recitation video on Similar Matrices (00:08:12)
Problem Solving: Similar Matrices
- Recitation video transcript (PDF)
Problems and Solutions
Work the problems on your own and check your answers when you're done.