# Advice for second rigorous book on linear algebra

Ashuron
Well,

I just finished a linear algebra course using David C Lay's book.
Thinking to go deeper on the subject.
I am never good with proofs, so I actually prefer books that may build some skills on that.
On that regard, the book perhaps should be fairly rigorous.

Right now I have several in mind:
-Algebra, Artin I may try to study this slowly...real slow
-Hoffman & Kunze seems rigorous
-Linear Algebra Done right, Axler seems packed with theory from the reviews

I have only looked into Artin's.
I do not plan to actually buy a new book, just want to study something from the library.

I am majoring in Physics, so relevant advices will also be nice.
If someone can actually tell me what is mathematical maturity and how to develop it, that would also be nice.

Homework Helper
Axler is fantastic. I'd recommend it.

Ashuron
Thank you nicksauce,

In general, can give you some more advice on how to tackle Axler's?

Staff Emeritus
Gold Member
I like Axler too. If you do a search (e.g. search the science book forum for "axler"), you will see that there are lots of these threads. In one of the recent ones, mathwonk said that he prefers Hoffman & Kunze because it covers more topics and includes more details. (I don't really see why one would want more topics).

How to tackle it? That's hard to answer. I like to work through a proof over and over, until I can do the whole thing in my head lying on the couch with my eyes closed, but I don't know if that's right for you. It might be better for you to try to get through the book as quickly as possible, and try to get the big picture before you study the details.

I'd say that mathematical maturity is the ability to think like a mathematician, but maybe there's a better way of explaining it than that. I think the only way to get it is to study more math, especially definitions and proofs.

Ashuron
Thanks a lot Fredrik,

Searched the physicsforum for several threads involving Axler..

The consensus seems to be Hoffman is comprehensive but Axler is much more an interesting read.

axeae
I thought Artin's textbook was more focused on abstract algebra. I would check out Axler's text or the texts by Shilov or Gelfand. The latter two are available as cheap Dovers now.

totentanz
Try this:
Introductory textbooks

Axler, Sheldon (February 26, 2004), Linear Algebra Done Right (2nd ed.), Springer, ISBN 978-0387982588
Bretscher, Otto (June 28, 2004), Linear Algebra with Applications (3rd ed.), Prentice Hall, ISBN 978-0131453340
Farin, Gerald; Hansford, Dianne (December 15, 2004), Practical Linear Algebra: A Geometry Toolbox, AK Peters, ISBN 978-1568812342
Friedberg, Stephen H.; Insel, Arnold J.; Spence, Lawrence E. (November 11, 2002), Linear Algebra (4th ed.), Prentice Hall, ISBN 978-0130084514
Hefferon, Jim (2008), Linear Algebra
Anton, Howard (2005), Elementary Linear Algebra (Applications Version) (9th ed.), Wiley International
Lay, David C. (August 22, 2005), Linear Algebra and Its Applications (3rd ed.), Addison Wesley, ISBN 978-0321287137
Kolman, Bernard; Hill, David R. (May 3, 2007), Elementary Linear Algebra with Applications (9th ed.), Prentice Hall, ISBN 978-0132296540
Leon, Steven J. (2006), Linear Algebra With Applications (7th ed.), Pearson Prentice Hall, ISBN 978-0131857858
Poole, David (2006), Linear Algebra: A Modern Introduction (2nd ed.), Brooks/Cole, ISBN 0-534-99845-3
Strang, Gilbert (July 19, 2005), Linear Algebra and Its Applications (4th ed.), Brooks Cole, ISBN 978-0030105678

Bhatia, Rajendra (November 15, 1996), Matrix Analysis, Graduate Texts in Mathematics, Springer, ISBN 978-0387948461
Demmel, James W. (August 1, 1997), Applied Numerical Linear Algebra, SIAM, ISBN 978-0898713893
Gantmacher, F.R. (2005, 1959 edition), Applications of the Theory of Matrices, Dover Publications, ISBN 978-0486445540
Gantmacher, Felix R. (1990), Matrix Theory Vol. 1 (2nd ed.), American Mathematical Society, ISBN 978-0821813768
Gantmacher, Felix R. (2000), Matrix Theory Vol. 2 (2nd ed.), American Mathematical Society, ISBN 978-0821826645
Gelfand, I. M. (1989), Lectures on Linear Algebra, Dover Publications, ISBN 978-0486660820
Glazman, I. M.; Ljubic, Ju. I. (2006), Finite-Dimensional Linear Analysis, Dover Publications, ISBN 978-0486453323
Golan, Johnathan S. (January 2007), The Linear Algebra a Beginning Graduate Student Ought to Know (2nd ed.), Springer, ISBN 978-1402054945
Golub, Gene H.; Van Loan, Charles F. (October 15, 1996), Matrix Computations, Johns Hopkins Studies in Mathematical Sciences (3rd ed.), The Johns Hopkins University Press, ISBN 978-0801854149
Greub, Werner H. (October 16, 1981), Linear Algebra, Graduate Texts in Mathematics (4th ed.), Springer, ISBN 978-0801854149
Hoffman, Kenneth; Kunze, Ray (April 25, 1971), Linear Algebra (2nd ed.), Prentice Hall, ISBN 978-0135367971
Halmos, Paul R. (August 20, 1993), Finite-Dimensional Vector Spaces, Undergraduate Texts in Mathematics, Springer, ISBN 978-0387900933
Horn, Roger A.; Johnson, Charles R. (February 23, 1990), Matrix Analysis, Cambridge University Press, ISBN 978-0521386326
Horn, Roger A.; Johnson, Charles R. (June 24, 1994), Topics in Matrix Analysis, Cambridge University Press, ISBN 978-0521467131
Lang, Serge (March 9, 2004), Linear Algebra, Undergraduate Texts in Mathematics (3rd ed.), Springer, ISBN 978-0387964126
Marcus, Marvin; Minc, Henryk (2010), A Survey of Matrix Theory and Matrix Inequalities, Dover Publications, ISBN 978-0486671024
Meyer, Carl D. (February 15, 2001), Matrix Analysis and Applied Linear Algebra, Society for Industrial and Applied Mathematics (SIAM), ISBN 978-0898714548
Mirsky, L. (1990), An Introduction to Linear Algebra, Dover Publications, ISBN 978-0486664347
Roman, Steven (March 22, 2005), Advanced Linear Algebra, Graduate Texts in Mathematics (2nd ed.), Springer, ISBN 978-0387247663
Shilov, Georgi E. (June 1, 1977), Linear algebra, Dover Publications, ISBN 978-0486635187
Shores, Thomas S. (December 6, 2006), Applied Linear Algebra and Matrix Analysis, Undergraduate Texts in Mathematics, Springer, ISBN 978-0387331942
Smith, Larry (May 28, 1998), Linear Algebra, Undergraduate Texts in Mathematics, Springer, ISBN 978-0387984551

Study guides and outlines

Leduc, Steven A. (May 1, 1996), Linear Algebra (Cliffs Quick Review), Cliffs Notes, ISBN 978-0822053316
Lipschutz, Seymour; Lipson, Marc (December 6, 2000), Schaum's Outline of Linear Algebra (3rd ed.), McGraw-Hill, ISBN 978-0071362009
Lipschutz, Seymour (January 1, 1989), 3,000 Solved Problems in Linear Algebra, McGraw-Hill, ISBN 978-0070380233
McMahon, David (October 28, 2005), Linear Algebra Demystified, McGraw-Hill Professional, ISBN 978-0071465793
Zhang, Fuzhen (April 7, 2009), Linear Algebra: Challenging Problems for Students, The Johns Hopkins University Press, ISBN 978-0801891250

Ashuron
well thanks a lot..
but the thread is quite old..
I settled to Axler's

@totentanz: How can one try 50 textbooks?

Ryker
@totentanz: How can one try 50 textbooks?
Yeah, I was meaning to ask how copying a random list of books seen somewhere is giving advice, but eh ...

totentanz
@totentanz: How can one try 50 textbooks?

And why do you think they put an index in the first pages? by the way they are just 33...

totentanz
Yeah, I was meaning to ask how copying a random list of books seen somewhere is giving advice, but eh ...

That is called "Decision Strategy"...when you have a menu on a resturant,you do not want to eat all what is in it,you just pick something that you are satisfied with,I know some people that read all the menu then ask you "What you are going to have??!"