What Are the Best Books for Studying Linear Algebra?

[bobydbcn]

Hello, everyone,
My major is physics.I want to study the representation of finite group and lie algebra. But I find my knowledge of linear algebra is limited, so I want to study further about invariant subspaces, projection operator, linear transformation, similarity transformation and so on.
Can you suggest me some good book about them? Thanks very much.

 

[Landau]

Roman's Advanced Linear Algebra is great, but it might be too advanced.

 

[Fredrik]

I like Axler, "Linear algebra done right". I have only read a small part of it, but I liked what I saw, and others have posted positive comments about it. You know, there's a whole science book forum here, with lots of threads like this one, so you should probably check those out to see what others have said.

 

[Landau]

Axler is good, but does not contain very much about projections and similarity tranformations.

 

[Newtime]

Linear Algebra by Shilov is dirt cheap and very dense. Encyclopedic almost, and a great thing to have around. also it's expensive, but for reviewing and understanding the core of linear algebra, Strang's book is great. if you want a bit more abstraction/more in depth look at what's really going on underneath all that notation, halmos' "finite dimensional vector spaces" is excellent.

 

[rochfor1]

I cannot recommend Lay's https://www.amazon.com/dp/0201709708/?tag=pfamazon01-20 enough for anyone wanting to learn the basics of linear algebra.

 

[bobydbcn]

Roman's Advanced Linear Algebra is great, but it might be too advanced.

It's a good book. It is a good book for who want to further study linear algebra.abstract and like an encyclopeadia. Thank you such much.

 

[bobydbcn]

I like Axler, "Linear algebra done right". I have only read a small part of it, but I liked what I saw, and others have posted positive comments about it. You know, there's a whole science book forum here, with lots of threads like this one, so you should probably check those out to see what others have said.

It's elegent and practical. Good book!Thank you so much!

 

[bobydbcn]

Axler is good, but does not contain very much about projections and similarity tranformations.

Thank you again!Hehe

 

[bobydbcn]

Linear Algebra by Shilov is dirt cheap and very dense. Encyclopedic almost, and a great thing to have around. also it's expensive, but for reviewing and understanding the core of linear algebra, Strang's book is great. if you want a bit more abstraction/more in depth look at what's really going on underneath all that notation, halmos' "finite dimensional vector spaces" is excellent.

It is a good reference for me to study the representation of lie algebra. Thank you so much.I will read it often!

 

[bobydbcn]

I cannot recommend Lay's https://www.amazon.com/dp/0201709708/?tag=pfamazon01-20 enough for anyone wanting to learn the basics of linear algebra.[/QUOT]
thanks a lot. it is a good book, maybe i will have a look at it soon.

 

[Fredrik]

For a quick intro to projection operators, I like pages 209-212 of Friedman's "Foundations of modern analysis". (Unfortunately page 212 isn't included in the preview, but maybe you can find it somewhere else).

For representations of Lie groups and Lie algebras, I like Brian Hall's book. He focuses on matrix Lie groups so you can read it without knowing any differential geometry. To learn those parts that require differential geometry I recommend "Smooth manifolds" by John(?) Lee, and/or "Modern differential geometry for physicists" by Chris Isham.

 

[Gauged]

Elements of Abstract and Linear Algebra, by E. H. Connell.

 

[bobydbcn]

For a quick intro to projection operators, I like pages 209-212 of Friedman's "Foundations of modern analysis". (Unfortunately page 212 isn't included in the preview, but maybe you can find it somewhere else).

For representations of Lie groups and Lie algebras, I like Brian Hall's book. He focuses on matrix Lie groups so you can read it without knowing any differential geometry. To learn those parts that require differential geometry I recommend "Smooth manifolds" by John(?) Lee, and/or "Modern differential geometry for physicists" by Chris Isham.

Thank you so much. Your suggestion is very constructive. I like to commuticate with you. I will send my email address to you.

 

[bobydbcn]

Elements of Abstract and Linear Algebra, by E. H. Connell.

thank you very much.But It must be a good book but I counldn't find it. It is really a pity.

 

[Gauged]

Elements of Abstract and Linear Algebra

 

[bobydbcn]

Elements of Abstract and Linear Algebra

Thanks you very much! I will read it.