What are the best resources for understanding Jordan Canonical Form proofs?

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SUMMARY

The discussion centers on resources for understanding the Jordan Canonical Form (JCF) of matrices, specifically focusing on proofs of its existence. A recommended website is provided, detailing a clear explanation of JCF: Teal GMU ECE Courses. Additionally, the notes for Math 4050 from the University of Georgia are highlighted as the best book for studying JCF. The Jordan Canonical Form is also noted for its utility in proving the Cayley-Hamilton theorem.

PREREQUISITES
  • Understanding of linear algebra concepts, particularly matrix theory.
  • Familiarity with the Cayley-Hamilton theorem.
  • Basic knowledge of eigenvalues and eigenvectors.
  • Experience with mathematical proofs and theorems.
NEXT STEPS
  • Research the detailed proof of the Jordan Canonical Form.
  • Study the Cayley-Hamilton theorem and its applications.
  • Explore additional resources on linear transformations and their matrix representations.
  • Review advanced linear algebra textbooks that cover Jordan forms in depth.
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Students of linear algebra, mathematicians, and educators seeking to deepen their understanding of Jordan Canonical Form and its implications in matrix theory.

joecoz88
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Does anybody know of any good websites that contain a clear proof of the existence of the Jordan Canonical Form of matrices? My professor really confused me today
 
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Incidentally, the Jordan canonical form makes it really easy to prove the Cayley-Hamilton theorem (which was assigned as a homework problem in our math methods class :p).
 

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