# Linear Algebra starter books

1. May 18, 2004

### Ebolamonk3y

Is there any titles that would aid a beginner into LA? Or just any good LA books that anyone knows of... Thanks in advance!

2. May 19, 2004

Texts for linear algebra

hi ,
one of the very good texts for starting linear algebra is:
LINEAR ALGEBRA AND ITS APPLICATIONS
BY : GILBERT STRANG.

3. May 20, 2004

### Ebolamonk3y

Strang?! MIT professor Strang? :) Its a bit expensive though.

4. May 21, 2004

### Tom Mattson

Staff Emeritus
Don't like the price? How does "\$0.00" sound?

http://crossspot.net/witno/notes/algebra2.pdf [Broken]
http://books.pdox.net/Math/Linear%20Algebra.pdf [Broken]

Last edited by a moderator: May 1, 2017
5. Jun 23, 2004

### styler

When i started i found two books to be very useful; i used them simultaneously:

Linear Algebra: Introduction to Abstract Mathematics

and

http://mathematicsbooks.org/0130198579.html

The first is a bit abstract but does a good job of opening you to abstract arguments and generalizations.
The second was the book from which i learned matrix operatios, the eigenvalue problem and other things that could be computed.
Start with it and after a month or so the open the Valenza book.
Once you know the basic theorems (of which there are few) the Valenza book can expose you to learning about the spectral thm, triangulation and inner products and the dual. These topics rarely get touched in the first (U.S.) linear algebra course and the they often get omitted from the second course wherein the student does proofs of the stuff in the first course. (ofte syllabi claim to plan to get to these topics but time invariably runs out )But all these topics are pretty important.

When you are ready to move on and need to learn cayley-hamilton thm and minimal polyomials and invariant subspaces and about quad forms and
similarity and Jordan form, nilpotet operators...etc..

then get:

Hoffman, Kenneth and Kunze, Ray. Linear Algebra
this book is excellent in exposition and its pretty comprehesive.
ow everybody always says you can't learn math without doing lots of problems. I ever found this more true than with linear algebra.

You can learn a thm but until you see and perform a calculation that illustrates it or uses it you never really learn its meaning. Linear algebra is a great subject to use for learing more serious mathematics and it has endless applications (A very well known mathematician once told me "my biggest problem is that i do'nt know enough linear algebra....you can ever know enough" this is a guy who many people would know...at first i laughed and then i realized how serious he was. now, he knows way more than is covered in these books but the point is to keep on with this subject if you are planing a career in science.)
But if you want to do that you will have to do much more than is expected of you in the standard courses at most universities.

Last edited by a moderator: May 1, 2017
6. Jun 24, 2004

### geometer

I think an excellent first book on Linear Algerbra is "Basic Concepts of Linear Algebra," by S. Isaak and M.N. Manougian from the University of South Florida. From the Preface to the book "The purpose of this text is to introcuce students of mathematics, the sciences, and engineering to the basic concepts of linear algebra." It assumes that you have completed a course in college algebra and trigonometry.

7. Jun 24, 2004

### fourier jr

for matrix theory:
Intro to Linear Algebra by Strang
Beginning Linear Algebra by Schaum's

for linear algebra:
Linear Algebra Done Right by Axler
& the one by Hoffman & Kunze

linear algebra for people who have already done it:
the linear/multilinear texts by Greub (Canadian content! )

8. Jun 25, 2004

### styler

I actually found this book to be confusing and not very useful when i first saw it. i have not looked at it since.
I am not sure why its so popular.

9. Jun 27, 2004

### robphy

Last edited by a moderator: Apr 21, 2017
10. Jul 12, 2004

### speeding electron

If you are teaching yourself, is Schaum's outline enough to learn form, or, as a suspect, does it work much better in conjunction with a more pedagogic text such as Strang's?

11. Jul 12, 2004

### styler

I take a different view of those schuam's outlines (and the other problem books like those by REA and those books by Walter Greiner) now that i have learne dmany of the subjects than i did when i was studying them.
I used to think they were a crutch and that if you needed them, you weren't really learning the fundamentals and if you used them you would be cheating yourself of understanding. Then i found the one on tensor calculus. That was the first time i realized how important it was to see exact calculations when text books lacked them. Later, discovering Greiner while learning basic QFT, I thought that it was great to see the long detailed calcuations but that there was a bigger picture i feard missing. Now with a beter grasp on these subjects i think t better to have a "serious" textbook around along with a problem book in the beginning/ In fact most of the math i know i learned from reading several books simulataneously. (usually at least one lower level book to accompany the main one i was trying to access and understand).

My advice now would be to get one of the books I mentioned and follow the chapters in it and the ones that deal with similar topics in Schaum's simultaneously.
Linear algebra is not a very deep subject but its subtle power is sometimes unapprecuated by the student. It can do all sorts of things. And every important theorem is directly related to somehting that can be calculated so its important to be proficent with systems of equations and matrix operations and details of definitions of the various algebraic objects to fully absorb the power of the theorems.

I guess it depends on why you want to learn the subject. If you just wanted to pass one of those freshman linear lagebra classes it might be enough. If you want to go on and learn more mathematics though, you will need much more than the Schuam's outline.
I'd seriously consider getting the Bretcher book (see above post) and using it conjointly with Schuam's if i were you.

12. Jul 26, 2004

### theFuture

I'm using Linear Algebra - Messer next year. I've heard bad reviews. How would you compare it to the other books recommended (especially at stressing theory and proof techinques)?

13. Sep 16, 2004

### mathwonk

i recommend all books by serge lang. he has (at least) one on linear algebnra.

14. Apr 22, 2006

### bash_b

i need tat LA BY GILBERT STRANG PDF

i need the LA BY GILBERT STRANG ebook... plz send me the link...