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I am looking for a Linear Algebra text for a beginner that goes about the subject in a mathematically rigorous fashion and at the same time respects the geometric intuitions behind Linear transformations and so forth.

I am interested in proof based text , mind you this will be my first encounter with linear algebra so are there any texts fulfilling the a aforementioned requirements?

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    $\begingroup$ Friedberg, Insel and Spence is a good book. $\endgroup$ – littleO Jul 18 '17 at 23:16
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    $\begingroup$ Linear Algebra Done Right by Sheldon Axler $\endgroup$ – Jonathan Davidson Jul 18 '17 at 23:19
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    $\begingroup$ I have looked at Axler my only contention is that the author say that it is meant to be a second course can i still use the book regardless $\endgroup$ – Atif Farooq Jul 18 '17 at 23:20
  • $\begingroup$ Both references given are great! I would also add Meyer's book. (Matrix Analysis and Applied linear algebra) $\endgroup$ – Joaquin San Jul 18 '17 at 23:21
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    $\begingroup$ The one and only: Finite-dimensional vector spaces by P. Halmos. As for the geometric intuition behind linear transformations, it can be acquired by looking at some examples; e.g., math.harvard.edu/~knill/teaching/math19b_2011/handouts/… Beyond dimension 3, however, it stops being "intuitive", and the knowledge of linear algebra (that should be gained from the above book) becomes our "eyes". $\endgroup$ – avs Jul 18 '17 at 23:24
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As suggested by @Jonathan Davidson Linear Algebra Done Right by Sheldon Axler is the book you are looking for, I know this because not long ago I was looking for the same thing you are seeking right now, and got that book suggested to me, read the contents and found out it's the one.

Here you can find Sheldon Axler himself explaining the topics of the book in his YouTube channel!! How wonderful is that!!

Here you can find the solutions to the exercises in the book.

This Lectures might help as well, among the books this course follow is Algebra Done Right.

One more thing: it's no wonder more than 200 universities world wide use that book for their Linear Algebra course.

Good luck learning the subject of Linear Algebra you'll have fun doing so.

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