Linear Algebra Textbook

I'm not quite sure which textbook to commit to since I can't seem to distinguish between them based on their individual merits and demerits.

It'd be great if someone could weigh out the merits and demerits (exercises, content, depth etc.) of both books.

Junaid Aftab asked Jul 7, 2016 at 18:41 Junaid Aftab Junaid Aftab 1,642 12 12 silver badges 33 33 bronze badges

$\begingroup$ This is not an answer, but this question over on MathOverflow may be of interest. In particular, one answer says that Hoffman & Kunze is "too advanced" for the questioner's needs. Another says that Friedberg, Insel and Spence is a "gentle introduction". So the books you are comparing seem to be at very different levels. I'm sure you can discern more by reading the answers and comments found at the link provided. $\endgroup$

Commented Jul 7, 2016 at 19:00 $\begingroup$ Use @SheldonAxler 's book! $\endgroup$ Commented Jul 7, 2016 at 19:03

1 Answer 1

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Hoffman and Kunze is the classic rigorous linear algebra textbook. My old mentor Nick Metas was one of the team of graduate students at MIT who worked over the manuscript of the original lecture notes for the course. The book is brutally mathematical with very few examples.That being said,it's very carefully written with many details in the proofs and definitions. If you're willing to work hard and you're serious about learning linear algebra as pure mathematics,you can hardly do better. But you'll need to supplement it for exercises and examples.

Linear Algebra by Friedberg, Insel and Spence is probably the single most comprehensive linear algebra textbook on the market. It's extremely careful with a ton of examples and it blends pure theory with applications very well.It's far more detailed and readable then Hoffman and Kunze and contains many applications you won't find in other textbooks, such as stochastic matrices. It also has many wonderful exercises. I just have 2 minor quibbles with it. First,in some ways,it's too comprehensive-to use the book in a course,even a year long course,one would have to be quite selective with it. Second-the section on the Jordan form and the diagonalization procedure is simply put, a trainwreck. This is a really important topic,so this really hurts the book.

answered Jul 7, 2016 at 19:01 Mathemagician1234 Mathemagician1234 17.5k 3 3 gold badges 60 60 silver badges 79 79 bronze badges

$\begingroup$ That puts things in perspective. In conclusion, which textbook would you recommend for a student of physics with a mathematical leaning? $\endgroup$

Commented Jul 7, 2016 at 21:10

$\begingroup$ @JunaidAftab If this is your first course in linear algebra, and noting that you're studying physics, I would definitely suggest you use Friedberg's book; by the point you need sophisticated tools to tackle more advanced theoretical physics, you'll have a solid grounding both theoretical and applied. If this is not your first time with linear algebra, I would offer you the following suggestion: get Hoffman & K's book and complement it with lecture notes from the internet (I'm assuming that you intend to buy only one book, so cost is a factor), they are usually more wordy and full of examples. $\endgroup$

Commented Jul 8, 2016 at 0:20

$\begingroup$ @EduardoM.Great. Would you know of any good online lecture notes/resources to complement Hoffman and Kunze's book? $\endgroup$