Linear Algebra Text

Question

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?

Answer 1

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.

Answer 2

There is a very famous book, at least in the French-speaking world, Linear Algebra and Elementary Geometry by Jean Dieudonné, Hermann, 1964 (it hasn't aged a bit). Written by one of the greatest topologists of the 20th century, it was nevertheless intended for secondary school teachers to teach the content to their students and is limited to dimensions 2 and 3. According to the criteria requested in the post , by far the best book I know.