Self study recommendations for a graduate linear algebra course?

Question

I´m looking for a book for self study about linear algebra for a graduate student. Basically in the course we want to cover the next:

• Vector spaces
• Linear transformations
• Inner product spaces
• Linear transformations between inner product spaces
• Jordan canonical form

Could you please recommend me a book for self study of this? Or could you please recommend me some online page of an advanced linear algebra course with some study guide or some homework assignments? I think that this option is the best because I can have a guide. Thanks.

Answer 1

I enjoyed reading

• Linear algebra done right
• Linear Algebra and Its Applications
• Advanced linear algebra

This one may be handy for your purpose

• Linear algebra problem book

Answer 2

The topics that you mention appears to suggest that this course will align more with a standard undergraduate-level proof-based course in linear algebra. As such, the best reference is probably Linear Algebra by Hoffman and Kunze. Many also like Linear Algebra Done Right by Axler.

Probably the main downside to the former is that the text is rather large and comprehensive and hence may not be well-suited to self study. On the other hand, this does make it a good reference book, especially after your linear algebra coursework has been completed. Another downside is that the text is much dryer than Axler.

A potential downside to Axler is that he tends to avoid the use of more sophisticated abstract algebraic machinery. This makes the reading more approachable, but if you already have experience with abstract algebra at the late undergraduate level, you might feel that it is unnecessarily restrictive, e.g. to restrict the conversation to vector spaces over $\mathbb{C}$ and $\mathbb{R}$.

One remark about Axler is that he takes a "determinant-free" approach. This can allow proofs to be far more illuminating, although one might feel that it comes at the cost of some computational power.

If I misinterpreted your comments and you are looking for a higher text, I personally like Advanced Linear Algebra by Roman. The start of this text rehashes many elementary results for review purposes as well.