Computing Jordan Canonical Form: An Example (Algebra 3: Lecture 6 Video 2)

Lecture 6: We started this lecture by discussing how to go between the invariant factors and elementary divisors of an F[x]-module.  We discussed an example computation of the Jordan canonical form of a certain 3 x 3 matrix.  We reviewed the Invariant Factor Decomposition Algorithm and talked about how to extend it to produce the Elementary Divisor Decomposition Algorithm.  We also briefly addressed how this algorithm gives a way to find the Jordan canonical form of an n x n matrix.  At the end of the lecture we discussed two problems that were closely related to examples we talked about in Lecture 4.  We emphasized why it is so important when working with Jordan canonical form that the field F contains all of the eigenvalues of the matrix A.

Reading: In this lecture we closely followed the second part of Section 12.3, pages 494-499.  The example we gave of diagonalizing the matrix xI-A  is a big part of Exercise 4 in Section 12.3.