Note to the Instructor

I have designed this module to be studied and completed by students in an introductory linear algebra course. Because it is a moderately hard project, I suggest having students work in teams. I have used the material as a supplemental project for teams of students who were able to work through the material on their own with little help from me. My students found the project to be an interesting application of linear algebra.

I suggest that you do two things before assigning the project:

  1. Read through the module yourself first, paying special attention to the Instructor's Notes to decide which parts of the project will best suit your class.
  2. Present a brief introduction to the singular value decomposition (SVD) to your students. SVD can be covered after other basic decompositions such as the LU or QR decompositions.

Pages 2 through 7 contain the heart of the lesson and become increasingly sophisticated with respect to mathematical content. Pages 4, 5, and 7 link to pop-up exercises and quizzes that test the student's knowledge and expand on the material in concrete examples. These exercises are where the real learning is done and should not be omitted. However, you can pick and choose the most attractive and relevant problems for your students.

If you'd like to learn more about the linear algebra methods used in traditional information retrieval, there are two excellent introductory references:

There's also a forthcoming text, Google's PageRank and Beyond: The Science of Search Engine Rankings (Langville & Meyer, 2006), that discusses the use of linear algebra in web information retrieval.