Can anyone suggest a linear algebra textbook?

[Rubicon]

I've seen loads of "what is the best Linear Algebra" threads but none quite match what I'm looking for. I'm currently using David Lay's Linear Algebra and its Applications, and I find the book readable, but strange.

He changes notations quite often and sometimes I have to try to figure out what he's talking about because his notations are different yet again. Also, his examples are not really illustrative of anything significant, are but simple calculations and step-by-step guides to how to solve problems.

I also find that it is not conceptually cohesive. I'm taking a summer course in Linear Algebra right now and it introduced a lot of terminology: "This is called x" but doesn't make it relevant what x actually signifies. As I progressed in math I found that a lot of the "jargon" are actually very meaningful, and I'm not getting that here, and the pace at which we're going only ensures that one day my ADHD brain will bet bowled over by all the terms. Maybe I'm missing the point, but I don't think he ties together concepts well.

I read a lot of good reviews on Shilov's book but also that it's not good for first-timers and wouldn't really be compatible with the course I'm taking- my professor pretty much lectures straight out of the book. Is there a good textbook that is more conceptual, but still accessible?

 

[Broccoli21]

Hey Rubicon, welcome to the physics forums!
I have read a bit of Lay's book, and am not a big fan of it. My favorite book on linear algebra is Axler's Linear Algebra Done Right. It provides plenty of motivation for the subject, and uses a clean, operator-theory approach that doesn't needlessly bring up matrices and determinants when they are not needed.

However, it is a pretty abstract treatment, in the classic theorem, proof, theorem, proof,... style. Are you looking for something with more physical or intuitive examples?

 

[dark_raider]

I second Axler, but as already noted he is not good for a first contact with LA. You could try Anton's elementary linear algebra for a gentler approach.

 

[Rubicon]

Thanks for the responses. Generally I like more intuitive examples. For some reason I have a hard time translating between theory and reality and physical examples always make me think of more variables than are relevant in the problem. I'm not very good at applied math and generally appreciate a more theoretical approach. I always "see" better when the examples are just points and lines, and when I think about things, even in other subjects such as history, I tend to see forces and light blots and colors.

 

[rezeew]

There are many linear algebra textbooks available, and it can be overwhelming to choose the right one. It is important to find a textbook that suits your learning style and aligns with the course you are taking. In your case, it seems like you are looking for a textbook that is more conceptually oriented and cohesive.

One textbook that is often recommended for its conceptual approach is "Linear Algebra Done Right" by Sheldon Axler. This book is known for its clear and intuitive explanations of concepts and its focus on understanding the underlying theory rather than just memorizing procedures.

Another option is "Introduction to Linear Algebra" by Gilbert Strang. This textbook is known for its visual approach and its emphasis on applications of linear algebra in various fields. It also has a companion video lecture series that can be helpful for visual learners.

Ultimately, the best way to find the right textbook for you is to browse through different options and see which one resonates with you the most. You can also ask your professor or other students in your class for their recommendations. Keep in mind that no textbook is perfect, and it is important to supplement your learning with additional resources such as online tutorials, practice problems, and study groups.