What would be a good book for learning Linear Algebra by myself?

[murshid_islam]

Summary: What would be a good book for learning Linear Algebra by myself in my situation (which is explained in my post below)?

I did an undergraduate Linear Algebra course about 18 years ago. The textbook we used was Howard Anton’s “Elementary Linear Algebra”. The problem is that I never really got a real understanding of what I was doing even though I still managed to get an A. I could follow certain methods of computing things like eigenvectors and stuff. Still, as I said, I didn’t understand the concepts behind them or why I was computing what I was computing, or what was happening under the hood of those calculations. As an analogy, consider someone being able to follow certain procedures and compute integrals without really understanding that they are calculating the area under a curve or a volume. That’s what happened with my linear algebra course. The only thing I do remember understanding is how the Gaussian elimination method could solve a system of linear equations.

Now I would like to really learn and understand the concepts behind the topics covered in a standard Linear Algebra course just for the sake of learning them. What would be a textbook or other resources like YouTube channels, etc. that would be appropriate for my needs?

 

[jedishrfu]

I would approach in a three prong fashion:

1) 3blue1brown on youtube has an excellent sequence on linear algebra with some great insight on what's going on

2) Khan academy and mathispower4u.com have excellent sequences covering all aspects of linear algebra in bite size 10 min chunks with problems worked and problems solved.

3) Schaum's Outlines has a great review book with many worked problems and many more unworked ones to try out.

You could use whatever book you're familiar with as either the primary or secondary as you work through the videos.

 

[fresh_42]

Another idea that usually gave me good results, is to search on Google with the key
"Linear Algebra"+pdf, or "Linear Algebra"+lectures+pdf

 

[swampwiz]

I would approach in a three prong fashion:

1) 3blue1brown on youtube has an excellent sequence on linear algebra with some great insight on what's going on

2) Khan academy and mathispower4u.com have excellent sequences covering all aspects of linear algebra in bite size 10 min chunks with problems worked and problems solved.

3) Schaum's Outlines has a great review book with many worked problems and many more unworked ones to try out.

You could use whatever book you're familiar with as either the primary or secondary as you work through the videos.

I took a deep dive into learning the Linear Algebra that I didn't understand the first go-round in college (somehow it wasn't formally covered in my Mechanical Engineering curriculum, although obviously it was introduced ad hoc in some courses). It's been a wonderful experience working out the proofs of such magic as the determinant of a product is the product of the determinants, finally grokking what nullspace is, and learning why certain matrices have a full eigensolution - i.e., that they are normal matrices, and that Hermitian, skew-Hermitian & unitary matrices are always normal, and that the "2-sided" eigenproblem of [ K ] { x } = λ [ M ] { x } only works if the matrices are both Hermitian (which corresponds to its eigenvalues being real) and that [ M ] have all positive eigenvalues, with the reason being that to transform this eigenproblem into a "1-sided" one requires that [ M ]^1/2 have real, non-zero eigenvalues (if an [ M ] eigenvalue is negative, that would introduce an imaginary component), and also only works because the product of Hermitian matrices is guaranteed to be Hermitian. (WHEW!)

The responder has given some great sources.

 

[murshid_islam]

I took a deep dive into learning the Linear Algebra that I didn't understand the first go-round in college ...

Which book(s) did you use?

 

[MidgetDwarf]

Depends on what your end goal is. That Anton book is one of the easiest introductions. I would work through it again, gaining familiarity with LA. Then use Lang: Linear Algebra with Berberian: Linear Algebra.

Books complement each other. Berberian's LA text is written in the style of Axler's : Linear Algebra Done Right, before Linear Algebra Done Right was written.

Lang goes through the determinant first approach, while Berberian goes through Linear Transforms first...

 

[swampwiz]

Which book(s) did you use?

I can't remember off-hand. I have all my books on an external drive that I'll have to dig up.

 

[mathwonk]

I have written about 5 sets of linear algebra notes, 4 of which are on my webpage:
https://www.math.uga.edu/directory/people/roy-smith

Namely notes 1, 3,e,f, 6c, and 7, My latest, and perhaps most suitable, one is not there, but you can contact me via private message if you want to know more. It is an expansion of note #1 above from 15 pages to 127 pages. It seems my notes are somewhat eccentric, and few people have given me any feedback on them so that they may be unreadable.

Thus perhaps a better option is the excellent notes of Sergei Treil at Brown:
https://www.math.brown.edu/streil/papers/LADW/LADW-2014-09.pdf

 

[malawi_glenn]

There are some good free PDF books on linear algebra here https://www.physicsforums.com/threa...-online-math-books-and-lecture-notes.1044710/

 

[WWGD]

Of course, if you don't want a strictly bottom-up approach, you cam use the search function here and look up solved problems. If you have access to a college library, drop by and look up, browse through the books the Linear Algebra section, see which one feels right. A rule of thumb I think helps is that the author has a careful index of notation used. It likely reflects that the author made an effort to be clear.

 

[murshid_islam]

you can contact me via private message if you want to know more.

Sent you a PM.

 

[mathwonk]

here is a link to the notes. see class notes #1, expanded version.
https://www.math.uga.edu/directory/people/roy-smith

 

[murshid_islam]

here is a link to the notes. see class notes #1, expanded version.
https://www.math.uga.edu/directory/people/roy-smith

Thanks a lot.