Introductory Linear Algebra Book Recommendation

I am looking for an introductory book on Linear Algebra. But the posts that I have found related to this question (for example this one) doesn't meet (neither address) my specific requirements. So I thought that it will not be a bad idea to post another question asking for introductory Linear Algebra texts. Some of my specific requirements are,

1. In the beginning of each chapter (at least most of the chapters), the book should discuss what were the main problems for which the necessity of idea(s) of the chapter was(were) needed.

2. The book should provide motivations for each (at least most) of the theorems.

3. Proofs should be very clear, rigorous and precise. In place of "jumps" some indication should be given so that "jumps" are indeed made.

4. The pace of the book should be slow.

5. The book's focus should be more (if not exclusively) on conceptual matters.

It may appear that I am claiming too much from the author. If that is so, then let me emphasize that it is not necessarily needed that all the requirements should be satisfied exactly but the more the book satisfies the requirements, the more better it will be for me.

Now let me tell some books that I really admire (though it may be that the books doesn't satisfy all the requirements I have given above) I don't like (at least for the beginners). I have marked the books I like by $(\color{green}{\checkmark})$ and those I don't by $(\color{red}{\times})$

Analysis

$(\color{green}{\checkmark})$ Analysis by Terence Tao.

$(\color{green}{\checkmark})$ Calculus by Tom M. Apostol.

$(\color{green}{\checkmark})$ Understanding Analysis by Stephen Abbott.

$(\color{green}{\checkmark})$ How We Got From There To Here: A Story of Real Analysis by R. Rogers and E. Boman

$(\color{red}{\times})$ A Course in Pure Mathematics by G. H. Hardy.

$(\color{red}{\times})$ Introduction to Real Analysis by R. G. Bartle and D. R. Sherbert.

Set Theory

$(\color{green}{\checkmark})$ Introduction to Set Theory by T. Jech and K. Hrbáček.

$(\color{green}{\checkmark})$ Elements of Set Theory by H. B. Enderton.

$(\color{green}{\checkmark})$ Abstract Set Theory by A. A. Fraenkel.

$(\color{green}{\checkmark})$ Foundations of Set Theory by A. A. Fraenkel.

$(\color{green}{\checkmark})$ Axiomatic Set Theory by P. Suppes.

$(\color{red}{\times})$ Naive Set Theory by P. R. Halmos.

Number Theory

$(\color{green}{\checkmark})$ Elementary Number Theory by D. M. Burton.

$(\color{green}{\checkmark})$ Higher Arithmetic by H. Davenport.

$(\color{red}{\times})$ Introduction to the Theory of Numbers by G. H. Hardy and E. M. Wright.

The books listed under either $(\color{green}{\checkmark})$ or $(\color{red}{\times})$ doesn't follow any particular order of "liking" or "disliking".

Can you give some suggestions of Linear Algebra text books in accordance with my requirements as elaborated above?

Solution 1:

Sheldon Axler's "Linear algebra done right" is a good text, as probablyme said in the comments. Also I think "Linear algebra" by Jim Hefferon is a book that satisfies some of your requirements.