Week Program, Semester Week 11

Eigenvalues, Eigenvectors, and Diagonalization

This week concerns linear maps from a given vector space \(V\) to itself. We will investigate so-called eigenvalues and eigenvectors of such a linear map. These vectors have the neat property that the map simply maps the vector to a scalar multiple of itself. If sufficiently many of such eigenvectors exist within \(V\), then it is possible to choose an ordered basis such that the map can be written using a mapping matrix that is a diagonal matrix.

Key Terms

Eigenvalues, eigenvectors, and diagonalization.

Preparation and Syllabus

This week covers sections 11.1 through 11.3 from [11 - The eigenvalue problem and diagonalization]. Note that sections 11.4 and 11.5 are not a part of our syllabus.

Exercises

Exercises for Long Day.

Exercises for Short Day.