# Is this a bad linear algebra text?

Critique this linear algebra text

Micromass has said before that there are a bunch of bad linear algebra textbooks out there. So someone linked me before to a free linear algebra text and I wanted to ask the forum community's opinion of it.

http://joshua.smcvt.edu/linearalgebra/book.pdf

Its a pdf site, it should take at most a minute to load.

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mathwonk
Homework Helper
i took a brief look, at the beginning of chapter 3, where he discusses isomorphism, and at the sections where he defines bases and dimension. i would ay this is a pretty good book for getting some understanding of what the ideas mean, since he gives a lot of examples.

on the theoretical side, the fact that he defines isomorphisms and discusses the concept with examples is good. the fact that he actually proves that all bases have the same dimension is a sound plus for his rigo as well.

having said that, i might criticize slightly the presentation of some of the statements and proofs of things. e.g. the important lemma 1.16 is poorly worded, and the big proof i mentioned above of cardinality of bases might not be that easy to read, although the logic is correct.

but i think this seems like a good starter book.

Gold Member
I've linked this text before as an example of what I feel to be a good free LA text. I agree with mathwonk; it's for an introductory course.

You might want to check the library for Axler's book: Linear Algebra Done Right. It does not assume a previous course in LA and is more rigorous, if that's what you're looking for.

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i took a brief look, at the beginning of chapter 3, where he discusses isomorphism, and at the sections where he defines bases and dimension. i would ay this is a pretty good book for getting some understanding of what the ideas mean, since he gives a lot of examples.

on the theoretical side, the fact that he defines isomorphisms and discusses the concept with examples is good. the fact that he actually proves that all bases have the same dimension is a sound plus for his rigo as well.

having said that, i might criticize slightly the presentation of some of the statements and proofs of things. e.g. the important lemma 1.16 is poorly worded, and the big proof i mentioned above of cardinality of bases might not be that easy to read, although the logic is correct.

but i think this seems like a good starter book.
Thank you!

I've linked this text before as an example of what I feel to be a good free LA text. I agree with mathwonk; it's for an introductory course.

You might want to check the library for Axler's book: Linear Algebra Done Right. It does not assume a previous course in LA and is more rigorous, if that's what you're looking for.

Thanks again!! I might use the free linear algebra book at first and then come back later for a more rigorous treatment. Mostly because I doubt my school's library has the book. But I'll check.

Gold Member
Thanks again!! I might use the free linear algebra book at first and then come back later for a more rigorous treatment. Mostly because I doubt my school's library has the book. But I'll check.

No problem.

If your university doesn't have it, you can probably find an inexpensive copy on abebooks.

micromass
Staff Emeritus
Homework Helper
It looks like a pretty decent book. I think the book gives a lot of motivation for the subject and it treats the subject generally enough (i.e. with respect to vector spaces and stuff.

No problem.

If your university doesn't have it, you can probably find an inexpensive copy on abebooks.
Thanks, at the moment though money is not on my side!

It looks like a pretty decent book. I think the book gives a lot of motivation for the subject and it treats the subject generally enough (i.e. with respect to vector spaces and stuff.

Okay thanks, I've already started reading through the text and I like it so far. There is a test in Physics I next week for me.. who knows, maybe the first couple chapters might help me. =D

So someone linked me before to a free linear algebra text and I wanted to ask the forum community's opinion of it.
This is a great free math textbook. I used it a fair bit a few years ago, and I think he has updated it since then. It even has a solutions manual available, which many free books do not have. If you find it moves too fast at any point, the online notes here are a good refresher of basic concepts:
http://tutorial.math.lamar.edu/Classes/LinAlg/LinAlg.aspx

Axler's book is a good follow-up (or a supplement) to Hefferon as it is more theoretical and does not get bogged down in too much matrix manipulation.

Edit: Just to add that Ben Crowell has reviewed Hefferon's book here:
http://www.theassayer.org/cgi-bin/asbook.cgi?book=29

And there is another review here:
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review

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This is a great free math textbook. I used it a fair bit a few years ago, and I think he has updated it since then. It even has a solutions manual available, which many free books do not have. If you find it moves too fast at any point, the online notes here are a good refresher of basic concepts:
http://tutorial.math.lamar.edu/Classes/LinAlg/LinAlg.aspx

Axler's book is a good follow-up (or a supplement) to Hefferon as it is more theoretical and does not get bogged down in too much matrix manipulation.

Edit: Just to add that Ben Crowell has reviewed Hefferon's book here:
http://www.theassayer.org/cgi-bin/asbook.cgi?book=29

And there is another review here:
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review
The notes look very nice thanks! I'll try to visit the sight here and there, though I'm the very stubborn type that likes to figure it out the hard way ahah.

And thanks Dembadon again for the recommendation. ^.^

From the preface, it looks pretty good to me. It's about what we did in my intro LA course--my school used it as a transition from computational math to theory as well. I think our prereq was Calc II, but it seems to be basically the same deal. We used a text one of our professors had written, though, and the school just passed it out to us in Mathematica files. I wish I still had it to study from, so maybe this'll be a good substitute next time I need to review. But yeah, it looks fine.

mathwonk