• Scalar fields other than $\mathbb{R}$ and $\mathbb{C}$.
  • Precise. Visual explanations are good, but they must complement definitions and proofs, not replace them.
  • No repetition of text. It may reference other textbooks for linear algebra, order theory, etc.
  • Modern. Semilinear transformations, category theory.
  • Well-known prerequisites. Phrases “it is a well-known fact” and “it is evident” without references must occur as rarely as possible.

There was a similar request, but concentrated on problem-solving, not on slick theory. Some examples I found so far:


This book by Gruenberg-Weir seems to be what you are after.

All spaces are over arbitrary fields (but $\mathbb R$ and $\mathbb C$ are given extra consideration), the book is rigorous, self-contained, contains many drawings,studies semilinear transformations, is fairly advanced and has a key to the exercises at the end.

And it is very cheap.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.