Linear Algebra Text Recommendation

  • #1
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  • #2
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Any thoughts? I am thinking of just getting whatever is cheaper :/
 
  • #3
Fredrik
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I'm sure either one is a good choice. I would go for Axler's book myself. I have only read a few pages in it, but I got a very good impression. Others have recommended it here in the forum as well. Tip: Use the "search this forum" feature.

You don't need to know any calculus to study linear algebra (don't expect to see any derivatives in these books; linear algebra is about linear operators between finite-dimensional vector spaces), but you need to know a little linear algebra (just a little) to study multivariable calculus.
 
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  • #4
thrill3rnit3
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I was going to suggest Serge Lang's Linear Algebra text, but since it isn't one of the choices, I'll have to go with Axler as well.

I haven't read Halmos's text personally, but I've read Axler's recently, and it's pretty good.
 
  • #5
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I was going to suggest Serge Lang's Linear Algebra text, but since it isn't one of the choices, I'll have to go with Axler as well.

I haven't read Halmos's text personally, but I've read Axler's recently, and it's pretty good.
Well, I am quite open to suggestions as I have no experience in the matter.

I actually have two books already. One is the one on https://www.amazon.com/dp/0486660141/?tag=pfamazon01-20&tag=pfamazon01-20 publications. I had a really hard time reading just the first chapter.

And I also have one that is by https://www.amazon.com/dp/0521310423/?tag=pfamazon01-20&tag=pfamazon01-20 and I am not sure whether it is really comprehensive or not.

Any thoughts on the book by Hamilton?
 
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  • #6
thrill3rnit3
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I haven't really read Hamilton's book, but by looking at its table of contents and from other people's opinions, I can see that it's a bit lacking on some areas. It might be a good introductory book, but like I said, it's not "comprehensive" enough.
 
  • #8
thrill3rnit3
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I heard Strang's Linear Algebra is pretty decent.

I haven't read it myself, but I've seen his MIT lecture videos online, and they were amazing.
 
  • #9
Landau
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See here.
Ik don't think you can go wrong with either one of Axler, Hoffman & Kunze, Halmos, and Friedberg.
 
  • #10
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Are Halmos and Axler your only choices? I'd second or third (I didn't count) Hoffman and Kunze. I am reading it at present and the book is wonderful.
 
  • #11
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The Kunze book is a little pricey. I ordered Axler on the cheap, so if doesn't work out I'll just have to pony up and spend the money.
 
  • #12
Landau
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The drawback of Hoffman & Kunze is, for me, the old-fashioned typesetting. It makes it look more esoteric than it is. Axler is very modern, but covers less ground.
 
  • #13
thrill3rnit3
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How can I forget about Hoffman and Kunze?? Another great book.
 
  • #14
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Jim Hefferon's book is quite good and is free and provides a solutions manual as well for free. The downside is that it comes as a pdf.
 
  • #15
Landau
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How is that a drawback? You can print it...
 
  • #16
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Heh, you can get your hands on a lot of e-books if you know where to look. But printing can be expensive and possibly disorganized. You should check out the public library or better yet try to gain access to a university library.
 
  • #17
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If you want a cheap but good book, try another Dover book, the one by Shilov, although it's not everyone's cup of tea.
 
  • #18
Shilov, absolutely seconded. Even if you don't like it, it's only ten bucks or so, what's the big deal? Here's mathwonk's review of it:

I am choosing this book for my course on advanced linear algebra. This means nowadays a beginning course that covers all the bases, but that includes also some theory and proofs, and continues to the jordan form and spectral theorems.

I considered Axler, Lang, Hoffman Kunze, Halmos, and notes by Sharipov on the internet.

All these have their good points, but Shilov has it all: superbly clear explanations and proofs, examples and exercises, complete coverage of the important canonical forms, and a great elementary treatment of determinants, as well as tremendous attention to pedagogy.

E.g. like Halmos, Sharipov and some others, Shilov discusses nilpotent transformations separately and in detail, before doing jordan forms. since the idea of a jordan form is that every map is the direct sum of an invertible one and a nilpotent one, you would think it would make sense to discuss these types separately, but many books just cram the jordan form into one explanation with no discussion of nilpotent operators first.

finally, as a dover book, it is a terrific bargain. Friedberg Insel and Spence is a nice book, and Hoffman Kunze is also a classic, but those cost 10 times as much for about the same quality. I have reached the point in life where I will no longer assign a book that the publisher charges $135 for when there is a $15 book out there just as good or better.

Strangely however, not one student has ever expressed gratitude for this practice of mine in a class evaluation, but i suspect they appreciate it anyway, (or maybe Daddy is buying the books).

Edit: Having found cheap used copies of earlier editions of Friedberg et al..., I have relented and am using it also in my course. In general the earlier editions are better anyway. Some people have convinced me too that as clear as Shilov seems to me, it may be hard for some students to read. End of quote.

So, this may be a little bit abstract for you, but it's only ten bucks.
 
  • #19
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Shilov is most certainly not appropriate for self-study or for a first course.
 
  • #20
jasonRF
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Sorry to post to such a stale thread, but given your background I would suggest neither. I took the engineering calculus sequence in college, and it would not have prepared me for those books. I just worked through Axler myself, and although I love the book it clearly assumes that you know intro linear algebra (which I did). Almost all of hte exercises are proofs - I worked ~100 of them and I recall very few that weren't proofs. Even the preface states that it is for a second course in linear algebra. Halmos, and Hoffman and Kunze are at a similar level, if not even higher. If you are really gifted you may be okay starting with these, but most of us would quickly be discouraged.

I would recommend a true intro book - I think a used copy of an old edition of Anton's book would be hard to go wrong with. You can get them real cheap - I am familiar with the 8th edition and you can pick it up on Amazon for $5. Pay close attention to the chapters on abstract (general) vector spaces, linear operators, eigenvectors, inner product spaces, and complex vector spaces., as they are much more important than you might guess.

For e-books, I second the recommendation of Jim Hefferon's book - it even gives you a nominal schedule for a course, recommends a subset of the problems, and provides an answer book. If you are ambitious go this route. It is at a more advanced level than Anton but is written for people with no linear algebra background and is still within reach if you devote serious time and effort. Another free text worth a look is Linear Algebra Done Wrong, by Sergei Treil.

Good luck,

jason
 
  • #21
thrill3rnit3
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Shilov is most certainly not appropriate for self-study or for a first course.
And why is that?
 
  • #22
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For the absolute rank beginner, I do agree that the Anton book "Elementary Linear Algebra" is the best. People seem to think that the later editions arent as good. I personally have the 7th edition and I love it.

From Anton you can move up to the Friedburg or Shilov book.
 
  • #23
w-g
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Heh, you can get your hands on a lot of e-books if you know where to look. But printing can be expensive and possibly disorganized. You should check out the public library or better yet try to gain access to a university library.
You can get a printed copy of Hefferon's book (from lulu.com or even from Amazon)
 

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