Similar Matrices and Jordan Form

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Session Overview

Figure excerpted from 'Introduction to Linear Algebra' by G.S. Strang

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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