I'm looking for suggestions for linear algebra books, suitable for first year students, that emphasize linear transformations. Rigorous, with proofs and every detail, ideally starting out with concrete vector spaces, immediarely introducing linear transformations with lots of examples, a bit about linear subspaces, and then developing the subject under the motto "linear algebra = linear transformation theory", leading to abstract ideas and the usual material all presented as means to study linear transformations. Books along similar lines would be of interest.
Answer
You might want to take a look at Linear Algebra Done Right. The Table of Contents and other information about the book are available at www.linear.axler.net. Linear Algebra Done Right very much emphasizes the linear transformation approach, so it might be suitable for you.
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