# Linear Algebra Textbook Rec

Hi

I've got an introductory Linear Algebra course that is using Elementary Linear Algebra with Applications by Bernard Kolman, David R. Hill and from what I can ascertain, it's a garbagety textbook [https://www.amazon.com/dp/0130457876/?tag=pfamazon01-20&tag=pfamazon01-20]. A lot of of the negative reviews center around its lack of theory, bad examples and polarizing problems (either too easy/tedious or too hard given the material taught).

The course from what I garner is pretty computational but with a bit of theory and proofs. Are there any recommendations to an alternative introductory Linear Algebra textbook?

Thanks for any help!

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Hi

I've got an introductory Linear Algebra course that is using Elementary Linear Algebra with Applications by Bernard Kolman, David R. Hill and from what I can ascertain, it's a garbagety textbook [https://www.amazon.com/dp/0130457876/?tag=pfamazon01-20&tag=pfamazon01-20]. A lot of of the negative reviews center around its lack of theory, bad examples and polarizing problems (either too easy/tedious or too hard given the material taught).

The course from what I garner is pretty computational but with a bit of theory and proofs. Are there any recommendations to an alternative introductory Linear Algebra textbook?

Thanks for any help!
You want Strang's "Introduction to Linear Algebra." For more theory, supplement with Axler's "Linear Algebra Done Right" and if you prefer more rigor, Halmos's "Finite Dimensional Vector Spaces" is a classic.

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I think a book covering similar material at a similar level is:
http://joshua.smcvt.edu/linearalgebra/
available for free download and purchase on amazon.com. Axler is good if you don't want such a computational look at LA, and is also for beginners.

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I like Hoffman & Kunze - Linear Algebra.

jasonRF
Gold Member
I would recommend "elementary linear algebra" by Anton. It is a mix of computation and theory. I also second the Strang "intro to linear algebra" book for a first look at the topic. If you have never seen linear algebra before, I would not recommend Axler or Halmos unless you are prepared to do a ton of work learning things your current book may not emphasize - I would look at those after the course is over. If this is your second course in the topic, then both of those are reasonable references.

good luck

jason

jasonRF
Gold Member
I would recommend "elementary linear algebra" by Anton. It is a mix of computation and theory. I also second the Strang "intro to linear algebra" book for a first look at the topic. If you have never seen linear algebra before, I would not recommend Axler or Halmos unless you are prepared to do a ton of work learning things your current book may not emphasize - I would look at those after the course is over. If this is your second course in the topic, then both of those are reasonable references.

good luck

jason
forgot to mention that Axler explicitly states in his introduction that his book is for a second course, not for a first course. Halmos is at the same level as Axler.

jason

Fredrik
Staff Emeritus
Gold Member
forgot to mention that Axler explicitly states in his introduction that his book is for a second course, not for a first course. Halmos is at the same level as Axler.
Here's the exact quote:
Axler said:
You are probably about to begin your second exposure to linear algebra. Unlike your first brush with the subject, which probably emphasized Euclidean spaces and matrices, we will focus on abstract vector spaces and linear maps. These terms will be defined later, so don’t worry if you don’t know what they mean. This book starts from the beginning of the subject, assuming no knowledge of linear algebra. The key point is that you are about to immerse yourself in serious mathematics, with an emphasis on your attaining a deep understanding of the definitions, theorems, and proofs.
I studied an older edition of Anton for the linear algebra course I took during my first year at the university. I think I would have preferred Axler as a first book back then. I know I like it a lot better now. As I recall, Anton did a good job of teaching how to calculate stuff when the vector space is $$\mathbb R^n$$, but you could read at least 100 pages (maybe 200) without being able to explain what linear algebra is. I remember that it was actually possible to pass the exam we got without knowing anything about linear operators. :rofl: Axler on the other hand, starts chapter 1 with
Axler said:
Linear algebra is the study of linear maps on finite-dimensional vector spaces. Eventually we will learn what all these terms mean. In this chapter we will define vector spaces and discuss their elementary properties.
When I saw that, I instantly knew that I would like the book. (I understand that some people might prefer a different approach).

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For what its worth artin's algebra book has a lot of linear algebra in it. The frst 140 pages or so are dedicated to it as well as more topics throughout the book.

Has anyone ever used Linear Algebra: An Introductory Approach by Charles W. Curtis? How is it? We've been recommended this book for our Honours Linear Algebra class, but the professor said it isn't really necessary, so I was wondering whether it's actually worth going over it or even leaning on it heavily when studying.

I would seriously recommend you use Strang's Introduction to Linear Algebra concurrently
with the video lectures on M.I.T.'s website/youtube. As with any subject just one book is
never enough, ever, so I also suggest Serge Lang's Introduction to Linear Algebra.
I'm currently plowing these two together & I must say you have a perfect match, both
books go more or less over the same areas from two slightly different perspectives, Strang
giving it the ol' standard way while Lang lets you look at the same material slightly more
theoretically. In this case theoretically means that Lang gives you the tools to rederive
everything from the mere basics. I recommend both because with Strang you get a first
glimpse at the concept laying the cement and Lang is there to finish it off setting in stone the
concepts you'd just properly learned about from Strang

Forget Strang, it's so bloody boring. Stick with Lang, Serge's introductory book would
give you enough rigour to be able to approach Axler with confidence (assuming that's
the reason you're not already reading it like me :tongue:). Looking in Axler now I
understand way more from the casual glances. However I found Serge's Linear Algebra
book, the 2nd edition (not the third that's on amazon) and I must say I feel cheated.
This book contains the 3rd introduction to linear algebra, the 3rd Linear Algebra &
some stuff on groups and rings at the end (and answers at the back!).

mathwonk
Homework Helper
there are 4 free books on linear algebra on my webpage http://www.math.uga.edu/~roy/

#1 is only about 15 pages long and starts from scratch. Obviously there is a lot to fill in as "exercises".
#7 is about 67 pages long and also starts from scratch and is sort of a second course for advanced undergrads.

These first two treatments assume mostly polynomial algebra.

#3 is a complete introductory course on algebra including linear algebra and assumes very little but uses the abstract concept of a module over a ring.

#6 is a more condensed version of #3, also aimed at grad students.

These last two also treat groups and galois theory.

another free book is "linear algebra done wrong: by sergei treil, on his webpage.

I recommend this book. Also there is a superb book by shilov available in paperback.

the last page of my math 8000 notes, #6 above, has a list of references including some of those above.

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Hoffman and Kunze has treated me very well so far.

mathwonk