A lot of math textbooks are like this and people’s perception around them.
To be fair Axler’s linear algebra book states it’s for a second semester course in linear algebra but many math people recommend it as a first exposure to the subject to someone that doesn’t know any linear algebra anyway. Technically the only prerequisite is an exposure to proofs and mathematical thinking.
But the book doesn’t like determinants and isn’t focused on computing things around matrices and is instead focused on finite dimensional vector spaces and so on.
To someone that doesn’t even know what a matrix is but have seen some basic proofs it’d be hard for them to pick up and understand Axler in its fullest depth despite the prerequisites just being “math maturity”. Axler assumes you know a lot more than he writes, or assumes you’ll figure it quickly.
Same can be said for Rudin’s basic analysis book. Technically anyone can pick it up and go through it with minimum pre-reqs. But without a tutor or someone to answer questions most beginners would get stuck somewhere.
Also it’s a thing these books don’t tend to include any solutions so without someone checking your work or a proof assistant then most beginners wouldn’t have a clue if their proofs are valid or contain a subtle mistake or would think they’re valid but be incorrect.
In my honest view this is a bad example. Axler is a professor of mathematics and editor of multiple undergraduate and graduate mathematics texts series. His supervisor’s supervisor was Paul Halmos.
His books are introductory in the context of mathematics courses. They are not introductory in applied mathematical sciences contexts.
There I would suggest, e.g., Boyd and Vandenberghe’s Introduction to Applied Linear Algebra [1], Meyer’s Matrix Analysis and Applied Linear Algebra [2], Golub and Van Loan’s Matrix Computations [3] etc.
> But the book doesn’t like determinants and isn’t focused on computing things around matrices [...].
You are right. It is. I admit that I was trying to think of an introduction to numerical linear algebra, but I was unable to recall any titles I would personally recommend. That is why I tried to put it towards the end of the listed examples, as a progression of sorts.
I don’t think I can edit my comment anymore, but I am more than happy to improve future suggestions if you have any recommendations.
Maybe such books could provide recommendations for a good book as prerequisite?
E.g. "this book is for 2nd semester linalg, if you're not at that level yet or <whatever> we recommend <book X which can be assumed a baseline by this one>"
