Second Textbook in Linear Algebra after Strang

In summary, there is a recommendation for the book "Linear Algebra Done Right" by Shelden Axler, which is a shorter book that covers linear algebra with rigor and clear proofs. Another suggestion is "Advanced Linear Algebra" by Roman, which is a more dense and comprehensive graduate textbook. "Linear Algebra" by Peter Lax is also recommended, although it is expensive. Another option is "Linear Algebra Done Wrong" by Sergei Treil, which is available for free online. The conversation also mentions "Introduction to Linear Algebra" by Gilbert Strang, which introduces linear transformations before solving linear systems.
  • #1
Noxide
121
0
I used Gilbert Strang's text: Introduction to Linear Algebra, to introduce myself to the subject. The book drops off after giving a brief introduction to Linear Transformations. Can someone recommend a second text in Linear algebra that begins with Linear Transformations and develops the subject from there? I would prefer a more rigorous treatment, but the subject itself fascinates me and I would just like to continue onward from where I left off.
 
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  • #2
I like Axler. You can find other recommendations in the science book forum under academic guidance.
 
  • #3
Axler!
 
  • #4
I third Axler too. His book is short, so some people might think he omitted some other important concepts that should be covered in a second linear algebra course, but I think the book does a really good job tackling linear algebra with rigor. His writing style was great, proofs were pretty clear, and there were plenty of challenging (but good) problems in the book as well.
 
  • #5
While I definitely second all the Axler recommendations, I would also like to add Roman's "Advanced Linear Algebra." It's a grad textbook, so it's very dense and encyclopedic, but the first and second chapter (and third if you're interested) cover what you want in exceptional rigor.
 
  • #6
Luckily for you, there are lots of great books on linear algebra.

Linear Algebra Done Right by Shelden Axler

And perhaps complement that by

Linear Algebra- Shilov (a Dover) (Note: This was the first Linear algebra book that I learned from)

I like both books a lot.

A book from a algebraic perspective which I also adore is

Advanced Linear Algebra- Roman
 
  • #7
Also, Linear Algebra by Peter Lax is great (but expensive).
 
  • #8
Linear Algebra Done Wrong, by Sergei Treil might just be what you're looking for:
Another detail is that I introduce linear transformations before teach-
ing how to solve linear systems. A disadvantage is that we did not prove
until Chapter 2 that only a square matrix can be invertible as well as some
other important facts. However, having already de ned linear transforma-
tion allows more systematic presentation of row reduction. Also, I spend a
lot of time (two sections) motivating matrix multiplication. I hope that I
explained well why such a strange looking rule of multiplication is, in fact,
a very natural one, and we really do not have any choice here.

Not only does it look great but it's FREE:

http://www.math.brown.edu/~treil/papers/LADW/LADW.html
 

What is the purpose of "Second Textbook in Linear Algebra after Strang"?

The purpose of this textbook is to provide a more in-depth understanding of linear algebra concepts and their applications beyond what is covered in Gilbert Strang's introductory textbook.

Who is the target audience for this textbook?

This textbook is intended for students who have already completed a basic linear algebra course and are looking to further their knowledge in the subject, as well as for researchers and professionals who use linear algebra in their work.

What makes this textbook different from other linear algebra textbooks?

This textbook offers a unique perspective on linear algebra, with a focus on real-world applications and a more advanced level of mathematical rigor. It also includes numerous exercises and examples to reinforce the material.

Do I need to have read Strang's textbook before using this one?

No, this textbook can be used as a standalone resource. However, some familiarity with basic linear algebra concepts will be helpful in understanding the material.

What topics are covered in this textbook?

This textbook covers a wide range of topics in linear algebra, including vector spaces, linear transformations, eigenvectors and eigenvalues, diagonalization, and applications in fields such as physics, engineering, and computer science.

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