MTH 525, FALL 2006

Brief Notes for Week 9

(very tentative)

Monday, October 23

Assignment 6 is collected.

We begin chapter 6, on elementary forms. This begins a second major part of our course, looking at ways to classify linear transformations by finding just the right basis.
We define characteristic values (= eigenvalues) of a transformation and introduce the concept of diagonalizable.

Do p. 189:

We introduce annihilating polynomials.

Do p. 197.

Wednesday, October 25

We continue in chapter 6.

We develop the Cayley-Hamilton theorem (in section 6.3)

We introduce invariant subspaces (section 6.4)

Do p. 205.

We discuss triangulation, diagonalization, beginning section 6.5.

Last modified October 1, 2006