Jim Hefferon's Linear Algebra: A free textbook with fascinating applications

http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review

by hhm • 18 years ago

97 18 18 years ago

Dilpil• 18 years ago

It's a beautiful thing, linear algebra.

It looks like a nice book. My only criticism after a quick skim is that it seems to neglect stability issues (condition numbers, etc). I realize that that is technically linear analysis (and nearly all textbooks neglect it), but it still belongs in any intro book.

He touches on it slightly on page 68, but inadequately in my view. The issue is not that it's hard to program, but that the problem of ill-conditioned matrices is fundamentally hard.

Nevertheless, I like this book. I'll strongly consider using it in the event I teach linear algebra.

dangoldin• 18 years ago

Thanks. I'll take a look as soon I have time.

The direct links for the book: ftp://joshua.smcvt.edu/pub/hefferon/book/book.pdf

The direct link for the answers: ftp://joshua.smcvt.edu/pub/hefferon/book/jhanswer.pdf

rkowalick3• 18 years ago

I prefer books that are much the opposite, like Priciples of Mathematical Analysis. I like to fill in the gaps in terse presentations and poke around on the internet for applications and other things. A good professor, however, can make any book a good one.

I had a teacher last year that used Artin's Algebra. He made a game out of the massive amount of typos and errors:

Show that question X is false as stated. Give the correct hypothesis and prove the new theorem.

How can we strengthen question Y?

On page ABC, what is the error in the proof of such and such. How can it be fixed?

Honestly, any good professor can make even the worst of books enjoyable.

msie• 18 years ago

"I prefer books that are much the opposite, like Priciples of Mathematical Analysis. I like to fill in the gaps in terse presentations and poke around on the internet for applications and other things."

You are a special case. I think you can succeed in spite of the book being used. :)

rkowalick3• 18 years ago

I picked Rudin's book because it is infamously terse. It's an analysis/advanced calculus books with NO pictures at all.

wheels• 18 years ago

I think it really depends on how comfortable you are with mathematical symbols as a means of conveying something. I, for instance, tend to think of things very geometrically or algorithmically, so usually in understanding mathematics I have to visualize the application and work backwards. As such, the "applications" aren't so much a toolbox a la applied math as much as nice concrete examples that help me understand the underlying theory.

And for the record, another hat in the ring for Strang's Linear Algebra and its Applications.

plinkplonk• 18 years ago

"I prefer books that are much the opposite, like Priciples of Mathematical Analysis"

Can you recommend a similar book for Linear Algebra? (terse comprehensive rigorous).

Thanks in advance,

rkowalick3• 18 years ago

While it certainly isn't terse, Linear Algebra by Friedberg, Insel, and Spence is comprehensive and rigorous. It has everything you would ever want to know about linear algebra with some applications too.

antigravity• 18 years ago

(1) Axler's "Linear Algebra Done Right"

...a nice introduction to abstract linear algebra, but not quite abstract or terse enough.

(2) These course notes: http://www.math.mcgill.ca/goren/AlgebraII07-08/AlgebraII.htm

...good, though the duality section is a bit lacking. Riesz Representation Theorem FTW!

kqr2• 18 years ago

My favorite text on Linear Algebra is Gilbert Strang's Linear Algebra and Its Applications although the current edition is ridiculously expensive:

http://www.amazon.com/Linear-Algebra-Applications-Gilbert-St...

jimbokun• 18 years ago

I managed to find an older version of the book, but somehow still unused, for a much lower price. I haven't found anything missing yet that I really need to know. I'm sure Linear Algebra as a field of knowledge has advanced a lot in that time, but the basics are still the basics.

I bought it because I checked several Linear Algebra books out from the university library, including an even older version of Strang's, and found that I liked it far more than the rest. Good transitioning between motivation, explanation, proofs, and examples for each topic. Also, it follows the on-line Strang lectures.

uuilly• 18 years ago

We used Strang for Linear Algebra. It was the only math class in college I did badly in. I tried multiple times to understand linear algebra and every time I ended up at the picture in the first few pages of the book. Each page built upon the previous page and there were no pictures to anchor on.

A year later I took an OpenGL class then a grad class in Computational Geometry. Once I had pictures and application I was fine. Morphing space and w/ matrix transformations and drawing in it in OpenGL was all I needed to snap the semester of symbol manipulation into focus. Strang to me was like man pages. Great for reference, terrible for learning.

manny• 18 years ago

Looking at the Table of Contents it seems fairly decent.

The most helpful Linear Algebra book I have used is Linear Algebra by Friendberg, Insel, and Spence.

davo11• 18 years ago

Looks a good book. Would any readers know of a good book on more advanced linear algebar particularly all things eigen - eigenvalues eigenfunctions and so on theory and application, but not just lists of theorems (much like the recommended book)

charlesju• 18 years ago

I hated math in college, I never thought that any math past basic Algebra would ever be used again in my life. But as I progressed further in Computer Science, I learned that if anything, Linear Algebra is involved in so many cool fields; AI, Graphics, Searching, etc.

My biggest regret in college was not learning linear algebra as well as I should have, thanks for the great link.

dylan• 18 years ago

Always interesting to see if someone can write a great linear algebra book. I like Axler's "Linear Algebra Done Right" [1] because he puts off the determinant until it's clear why you want to define such a map. That the book continually treats the case when your field is the complex numbers slows things down at times, though.

[1] http://linear.axler.net

Jim Hefferon's Linear Algebra: A free textbook with fascinating applications

Related Stories