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 textbook.

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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