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
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Similar Matrices and Jordan Form (00:45:56)
Lecture 28: Similar Matrices and Jordan Form
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- Read Section 6.6 in the 4th edition or Section 6.2 in the 5th edition.
Problem Solving Video
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Similar Matrices (00:08:12)
Problem Solving: Similar Matrices
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Problems and Solutions
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