Linear Algebra Done Right

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I bought the hardcover edition: well-edited edition with few typos; the binding is excellent and durable (it does not gradually deteriorate during reading) and the pages are of good quality; the format of the book is very manageable.

From the point of view of contents, it proved to be an excellent introduction to linear algebra (vector spaces, linear maps, eigenvectors, eigenvalues ​​and eigenspaces and matrices) abstract and rigorous but also very concrete: each topic is accompanied by useful and illuminating examples and / or exercises carried out and many theorems are preceded by a short preamble that introduces their meaning and content at a discursive and informal level, facilitating the understanding of the more abstract aspects. Sometimes the proofs are left to the reader but these are always cases in which, if one has followed the book, such proof is within the reader's reach, being often analogous to that of other theorems demonstrated in the previous pages.
In addition, each section is accompanied by numerous useful exercises (not done!). The only venial flaw is that sometimes (although very rarely), the demonstrations proposed in these exercises are then considered preparatory to theorems presented in subsequent sections and this, in some way, forces us to go back to review the exercise and, if it has not already been done, to solve it.

The treatment of the theory of eigenvalues ​​is decidedly brilliant and original, developed without using the concept of determinant, which is then defined and explained only in the last pages even if the treatment of matrices is still carried out progressively as the abstract concepts become somehow applicable.

Sheldon Axler is a myth for rigor and clarity: in addition to this excellent Linear Algebra text, I recommend the text "Measure, Integration & Real Analysis" in the Springer Open Access series.

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