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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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  • $\begingroup$ I will refer you to this link math.stackexchange.com/questions/433858/… $\endgroup$ Commented Dec 20, 2017 at 7:12
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    $\begingroup$ Schaum's Outline of Linear Algebra $\endgroup$ Commented Dec 20, 2017 at 17:08

4 Answers 4

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Try Paul Halmos' Linear Algebra Problem Book.

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There are several options in addition to those already suggested in other answers:

  • Luis Barreira, Claudia Valls: Exercises In Linear Algebra. World Scientific, 2016. Each chapter contains a subchapter with solved exercises and a subchapter with proposed exercises.
  • T. S. Blyth, E. F. Robertson: Algebra Through Practice: A Collection of Problems in Algebra with Solutions. Volume 4. Linear Algebra. Cambridge University Press, 1985. Downside: rather expensive for its size.
  • John M. Erdman: Exercises and Problems in Linear Algebra. World Scientific, 2020. Downside: solutions aren't necessarily step by step.
  • Seymour Lipschutz: 3,000 Solved Problems in Linear Algebra. (Schaum's) McGraw Hill, 1989. This should not be confused with Linear Algebra by Lipschutz and Lipson, also in Schaum's ouline series, which contains 612 fully solved problems.
  • Fuzhen Zhang: Linear Algebra: Challenging Problems for Students. Johns Hopkins Studies in the Mathematical Sciences. Second edition. The Johns Hopkins University Press, 2009.
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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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The Berkeley problems also have a number of good linear algebra exercises. https://link.springer.com/book/9780387204291

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