The discussion centers around the topics typically covered in a linear algebra class, with a focus on self-study resources for physics and math majors. Participants share their insights on essential concepts and recommend textbooks for learning linear algebra.
Participants generally agree on the importance of certain linear algebra concepts for physics, but there is no consensus on a single best textbook, as multiple recommendations are provided.
Some participants note the omission of determinants in initial discussions, indicating that different resources may cover topics to varying extents.
This discussion may be useful for students in physics or mathematics who are preparing to study linear algebra independently, as well as educators seeking resource recommendations.
I should have mentioned determinants as well. If you understand these things, you're off to a good start. I've been told that Friedberg, Insel & Spence is a very nice book. Axler is also good. There are several other acceptable choices. I would however recommend that you stay away from books like Anton, which wait as long as possible with the introduction of linear operators (also called linear maps, linear functions or linear transformations). The sooner they are introduced, the better.Fredrik said:The concepts from linear algebra that you need to understand are: vector spaces, inner products, linear independence, orthonormal bases, linear operators, matrix multiplication, the relationship between linear operators and matrices, the adjoint operation, eigenvectors and eigenvalues.
bcrowell said:This is the best linear algebra book I know of, and it also happens to be free: Hefferon, http://joshua.smcvt.edu/linalg.html/ . "Best" for me means interesting applications and good motivation for new topics as they're introduced.