Reading materials and handouts

• A list of some applications of linear algebra.

A proof that an infinite-dimensional vector space has smaller dimension than its dual. A concrete example of an infinite-dimensional vector space that is not isomorphic to its dual. These arguments rely on the axiom of choice.

• Here is a nice article on tensor products, and here is a chapter from a book dealing with tensor products in detail. Here is a document explaining the role of the tensor product in quantum mechanics, and here is another, quicker explanation.

• Here is an article about universal properties.

• Here is an article about some cool uses of eigenvectors and eigenspaces (Fibonacci sequence, steady states). Here is a excerpt from a book on the same subject (population growth, differential equations, quadratic forms). Here is a webpage that explains the uses of eigenvalues in studying vibrations. Here is a presentation on uses of eigenvalues in statistics.

• A clip from the 1980 movie It's My Turn that shows how the Snake Lemma works.

• An article on how Google PageRank works, detailing some of the things we talked about in class. Here is another explanation.

• More on stochastic matrices.

• More on the Perron-Frobenius Theorem and some of its applications.