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Strang is simpler and clearer. Axler is more advanced in the sense that it doesn’t tie it to matrices. Strange is a “first course” book, Axler is a second cour

by dash2 2mo ago

Strang is simpler and clearer. Axler is more advanced in the sense that it doesn’t tie it to matrices. Strange is a “first course” book, Axler is a second course.

Tomte 2mo ago
Axler does limit itself to vector spaces over real and complex fields, though. That‘s fine, but I would have appreciated notices, which proofs and theorems do not hold in the general case. It‘s an exercise for the reader.
- fn-mote 2mo ago
  This is basically a request for a graduate course, though. Definitely not a first course in linear algebra. TBH, I don’t think there are surprises in the “general case” (whatever that is… modules over a PID??) that you can’t see by understanding the real&complex situation.
  - Tomte 2mo ago
    No, but a second course. Still firmly in undergraduate territory, second semester at my university. Most undergraduate linear algebra textbooks also contain this, unless they are matrix computation heavy (usually for the first course).
- seanhunter 2mo ago
  That’s not true at all. He does precisely the thing you want him to do and also gives a pedagogical justification in the preface. > This book usually develops linear algebra simultaneously for real and complex vector spaces by letting F denote either the real or the complex numbers. If you and your students prefer to think of F as an arbitrary field, then see the comments at the end of Section 1A. I prefer avoiding arbitrary fields at this level because they introduce extra abstraction without leading to any new linear algebra And the remarks at the end of 1A are that if you want to, you can think of F as an arbitrary field everywhere except the sections on inner product spaces and where the given field is C you can frequently also use any other algebraically closed field.
aureate 2mo ago
Depends how you think. I found Strang impenetrable and Axler simple and lucid. Some people seem to find abstract vector spaces weird and unmotivated without doing a load of stuff with lists and grids of numbers first. I find determinants weird and unmotivated without learning exterior algebra first. I wish Axler had been my first course.

by dash2 2mo ago

Strang is simpler and clearer. Axler is more advanced in the sense that it doesn’t tie it to matrices. Strange is a “first course” book, Axler is a second course.

Tomte 2mo ago

Axler does limit itself to vector spaces over real and complex fields, though. That‘s fine, but I would have appreciated notices, which proofs and theorems do not hold in the general case. It‘s an exercise for the reader.

fn-mote 2mo ago
This is basically a request for a graduate course, though. Definitely not a first course in linear algebra. TBH, I don’t think there are surprises in the “general case” (whatever that is… modules over a PID??) that you can’t see by understanding the real&complex situation.
- Tomte 2mo ago
  No, but a second course. Still firmly in undergraduate territory, second semester at my university. Most undergraduate linear algebra textbooks also contain this, unless they are matrix computation heavy (usually for the first course).
seanhunter 2mo ago
That’s not true at all. He does precisely the thing you want him to do and also gives a pedagogical justification in the preface. > This book usually develops linear algebra simultaneously for real and complex vector spaces by letting F denote either the real or the complex numbers. If you and your students prefer to think of F as an arbitrary field, then see the comments at the end of Section 1A. I prefer avoiding arbitrary fields at this level because they introduce extra abstraction without leading to any new linear algebra And the remarks at the end of 1A are that if you want to, you can think of F as an arbitrary field everywhere except the sections on inner product spaces and where the given field is C you can frequently also use any other algebraically closed field.

aureate 2mo ago

Depends how you think. I found Strang impenetrable and Axler simple and lucid. Some people seem to find abstract vector spaces weird and unmotivated without doing a load of stuff with lists and grids of numbers first. I find determinants weird and unmotivated without learning exterior algebra first. I wish Axler had been my first course.