MATH 308 I and J: MATRIX ALGEBRA

Resources

Alternatives to the Book

While we will cover most of Holt in order, the underlying mathematics is quite old and there are many other expositions. A few:

• My lecture notes (UW NetID required). These are not pretty or well-edited; they are written with only myself as the audience in mind. They may be modified at any time.
• S. Paul Smith has extensive and reasonably well-edited notes which are written at a somewhat more advanced level than Holt. See the "sermon" at the end as well.
• Natalie Naehrig has some perhaps friendlier notes, which are not quite as polished.
• Alex Young has turned the course into a series of "Paul's online math notes"-style pages.
• Khan Academy has extensive material at this level, like this.

Proofs

Linear algebra is at once extremely practical and quite abstract. Its theoretical underpinnings will be presented in lecture, frequently with proofs. Homework will often give you practice with hands-on examples, which later courses will build upon. Deciphering proofs is thus part of the course if you are to learn the material deeply. So, we will spend a small amount of lecture time early on discussing proof strategies.

You will be expected to produce some proofs on exams. To successfully construct proofs may require a change in your perspective. Being "mostly right" is fine in much of life, but not when writing proofs. Misunderstanding a definition or forgetting to check an assumption on a theorem can turn your argument into complete nonsense. Here are some examples from students of the difference between "mostly right" definitions and fully rigorous ones.

Proofs

See the example proofs document.

Inverses

Here is a summary of the course's material on inverses.

Diagonalization

Here is a summary of the course's optional material on diagonalization.