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After posting this question, I have decided to separate the contents into multiple questions.

Reasons I am doing this:

  • Right tag for each topic, so people who are interested in that topic and watch that tag may suggest rather than one suggests books for all the mentioned topics. So it might be simpler and more efficient.

  • Having difficulty to decide as everyone has his own opinion. But I believe there is something common for most of people who have read in this topic.

  • I did not get many answers to see common suggestions and take a decision.

  • So this post might be as voting post.

I need a book in:

$\big( \bigstar \big)$ $\text{Linear Algebra}$:

Some suggestions in this website are:

$\star$ "$\text{Linear Algebra}$" by "$\text{Friedberg, Insel and Spence}$".

$\star$ "$\text{Linear Algebra}$" by "$\text{Serge Lang}$".

$\star$ "$\text{Introduction to Linear Algebra}$" by "$\text{Serge Lang}$". (different from the previous one).

$\star$ "$\text{Linear Algebra}$" by "$\text{Kunze Hoffman}$".

$\star$ "$\text{Linear Algebra Done Right}$" by "$\text{Sheldon Axler}$".

$\star$ "$\text{Linear Algebra Done Wrong}$" by "$\text{Sergei Treil}$".

Even though I have some knowledge in this topic, I want a book that is easy to read for self-learners, to be as comprehensive as possible (but starting from scratch, so it should not be 2nd text), contains proofs as much as possible, contains good number of examples/exercises, and requires least prerequisites.

Someone suggested

$\star$ "$\text{Linear Algebra Done Right}$" by "$\text{Sheldon Axler}$".

But I am not sure if it satisfies the above criteria.

Another one commented: "Linear Algebra Done Right is amazing as a 2nd text, I wouldn't recommend it as a first entry to anyone except those who had a strong theoretical math background."

You can suggest other than the listed above if you think there is a better one, please suggest the best (one book) (in your opinion). Thanks a lot.

anomaly
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Hussain-Alqatari
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    Shilov's Linear Algebra hasn't much hype around it, but I think it's a solid choice. – user1551 Sep 01 '22 at 18:39
  • I kind of agree with a comment from one of your other similar questions. One shouldn't decide on just one book. One should use many books as resources when learning a subject. Often times when you finish one book, you can get through the rest of the books much quicker because you understand the subject better. So the most important thing is to just, get started on one book and try to get as far as possible... Common sense says to start with the "easiest" book - which in my opinion is usually the one with the longest explanations. Concise books like Rudin PMA tend to be harder. – Adam Rubinson Sep 01 '22 at 19:30

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