Unit III: Positive Definite Matrices and Applications

Similar Matrices and Jordan Form

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Session Overview

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.

Session Activities

Lecture Video and Summary

Suggested Reading

  • Read Section 6.6 in the 4th edition or Section 6.2 in the 5th edition.

Problem Solving Video

Check Yourself

Problems and Solutions

Work the problems on your own and check your answers when you’re done.

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Course Info

Learning Resource Types

theaters Lecture Videos
grading Exams with Solutions
notes Lecture Notes
theaters Recitation Videos
assignment_turned_in Problem Sets with Solutions
laptop_windows Simulations
groups Course Introduction
co_present Instructor Insights