2025-11-18

This following is a very brief summary of what happened in class on 2025-11-18.

Working with two explicit examples, we analyzed a second, optional canonical form of a matrix, called the Jordan canonical form. This form is basically the consequence of using the Chinese Remainder Theorem to further decompose the summands in the Invariant Factor Form decomposition.

Next class we'll fill in the details for how this works in general.

Concepts

• Rational Canonical Form III - Computation
• Jordan Canonical Form I - Definition
• Jordan Canonical Form II - Computation

References

• Dummit & Foote, Abstract Algebra: Section 12.3