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Requirements:

  • 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:

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1 Answer 1

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.

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