Linear Algebra Book for Math Majors at MIT

This Linear Algebra book was written for math majors at MIT. This is an old school classic!

The book is called Linear Algebra and it was written by Hoffman and Kunze.

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[asstube]

Absolute classic! In same league as Ahlfors for Complex, Coddington for ODE, Artin for Algebra, Buck/Kaplan for Advanced Calculus, Munkres for Topology, Froberg for Numerical Analysis, .... They are still in print n immortal.

[tomcalderaro]

I appreciate your comments on 'reading for enjoyment'. It's something that easily gets lost.

[pgray]

Once again you’ve reviewed one of the books I used in undergrad. UofM, Winter 1967, Math 513, Prof. James Kister. Good teacher. Good book.

[thesakeofitname]

Linear Algebra bu Hooffman is really nice book (a gem) from an engineering point of view. I didn't offically read it but most of its topics were covered on a similar layout in our engneering linear algebra and linear system theory courses. It's sufficiently rigorous, clear, and practical in constrast to other *abstract* books : -)) Linear algebra books generally tend to be practical and applied though...

[eliasmai]

My university used to use this text for our sequence of two semester linear algebra text for math majors. But it switched to Insel, Friedberg and Spence's Linear Algebra about twenty years ago.

[johubify]

When I say I love reading, people always misunderstand me for reading literature, lol, but I actually love reading math books.

P.S: I'm tense, they barely started online classes 3 weeks ago and now BAM, they give half the book in the test we're gonna have 3 days later.

[johndorsey]

I'm a huge fan of Intro to Linear Algebra with Applications by Steven Roman. The book has been out of print for a long time, but I think it's the best math, physics, or chemistry textbook I've ever used. My college didn't offer a Proofs course. Instead Roman served as the link between computation-based classes like calculus and advanced proof-based courses like abstract algebra with a good mix of computation and proof problems. Many of the computation problems have answers in the back (but no solutions). The notion of abstraction is introduced about midway through the text in the chapter on vector spaces. Each section is well motivated with the author clearly explaining its place in linear algebra. One downside is the author only considers real matrices.

[nmzgoio]

Yeah！This is a great book of linear algebra ！It is popular！( Especially for those who major in pure math. )

[pinklady]

I will check out that book. Thanks for mentioning it.

[OleJoe]

I have that book as well as Gilbert Strang's. Strang is also a professor at MIT. Strang's book is more humane, plus he has a whole LA course using his book on YouTube.

For myself, I've always found that getting an understanding of concrete examples and computations first, made learning the abstract ideas and proofs easier.

Trying to understand the abstract first is much harder.

One thing I've noticed about H&K. In the Jordan decomposition section they put the generalized eigenvectors is the opposite order of most other books, which causes the order of the Jordan blocks in the Jordan matrix to be different.

Another book on linear algebra I just got, uses n×m matrices, rather than m×n. So, in the SVD A=USV*, you get U as an n×n, S as a n×m and V as a m×m, instead of the other way around.

Stuart's book from 1973, even has the SVD as A=VSU*, which can be really confusing. Here I used S for capital sigma.

[thelastcipher]

Kolman's and Shifrin's gives more geometric intuition.

[ShinXiao]

linear algebra is always an interesting subject. I got into it and took a course on it because of quantum mechanics but I still don't fully understand vector spaces

[justbargelle]

wow posted an hour ago. i am searching for the same I used to be so good at, my son is on his 8th grade now and I fell like i dont know how to teach him now coz of the common core math lol.

[OleJoe]

To comment a second time. I really feel that linear algebra is underrated. It's importance to modern mathematics cannot be overstated.

I might even venture to say that a knowledge of linear algebra is more important than calculus in today's world.

[leonardobranco]

when you read books as a hobby, do you take notes or just read? you are a great source of inspiration!!!

[WitchidWitchid]

Looks a bit like Serge Lang's "Linear Algebra" book which is also a theoretical text and the first Linear Algebra book I used. When I read a math text I am the type who will work on every section until I understand it. It takes a bit longer to cover the entire book but IMHO it is worth the extra time spent. However, everyone has different approaches that work best for them. BTW, to me 1961 is not old, but that's because I was born in the 1950s so everything that comes after my DOB seems recent/modern to me. LOL :)

[mdfk]

This one's definitely rigorous and old school! I first saw it in my college library, a late 80s copy in a dusty and pitiable state out of neglect, as David Lay has long replaced it as standard introductory text.
Needless to say, I was unable to understand anything the first time I read it. Now however, I own a copy and am using it for a more advanced course in linear algebra. I find it an absolute pleasure to read, the way definitions are presented and proofs motivated is delightful. But I do feel that their proofs are usually unnecessarily technical and complicated, as compared to other texts.
Btw, can you plz do a review on Advanced Calculus by Loomis and Sternberg? I've heard wonderful things about it, that it's extremely detailed and comprehensive (and very difficult too!).
On finding that it's pdf is freely available online, curiosity led me to download this beast, and boy! was my mind blown! I would like to know what the sorcerer thinks about this magic book😋.
On a related note, guess which book is mentioned in linear algebra additional reading of Loomis and Sternberg? None other than Hoffman and Kunze🤩.

[robertmorrison]

I like your series where you cover a bunch of different math books, even though I don't study most of the subjects in the books. Can do a differential geometry book at some point? That would be kind of cool.

[jonathanratcliff]

How does it compare to Friedberg's book? I always found his textbook to be extremely readable (which we all know is a luxury when it comes to math books).

[antoniollopis]

Could you make a video about a review of the book titled Ordinary differential equations, by Morris Tenenbaum and Harry Pollard? Thanks in advance.