Welcome to Week 9.
Our main theme this week is eigenvectors – what they are, why they are important, how to find them and why they might not always exist in sufficient numbers for us to be able to diagonalize a matrix.
In Lecture 17, we will discuss the main definitions and also look at the maximum number of distinct eigenvalues that can occur. This will lead us to the characteristic polynomial of a matrix and to the concepts of geometric and algebraic multiplicity, which will be discussed in Lecture 18.
Slides for Week 9.
Here is (an old version of) Lecture 17.
Here is Lecture 18.
Relevant sections of the lecture notes this week are Sections 3.3, 3.4 and 3.5.