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I'm going to find some Exercise books in linear algebra and I was wondering if there are some exercise books (that is, books with solved problems and exercises) The books I'm searching for should be:

  • full of hard, non-obvious, non-common, and thought-provoking problems;
  • rich of complete, step by step, rigorous, and enlightening solutions;

Thanks in advance

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Try Paul Halmos' Linear Algebra Problem Book.

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The book you are looking for is Problems and Theorems in Linear Algebra (Translations of Mathematical Monographs, Vol. 134) Paperback – June 13, 1994 by V. V. Prasolov. There is much fuller second edition, but as far as I know it was not translated (yet) into English.

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