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 28: Similar Matrices and Jordan Form
Problem Solving: Similar Matrices
Work the problems on your own and check your answers when you're done.