

What do you want to know about Linear Algebra? - ColinWright

I regularly see Linear Algebra mentioned here, and I usually gloss over it because I figure that what people want to know is more advanced than I could help with.  But a recent conversation, and an equally recent set of comments here on HN (which now I can't find - typically) have made me re-assess this point of view.<p>It seems that what some people want to know is what I think of as completely elementary.  I very much doubt that I'd be very good as a teacher in a distance learning context - I have a healthy scepticism about my abilities in that direction - but there are people here who know a lot about linear algebra, and maybe they can chip in with observations, visualizations, and references to help those who want to know more.<p>So, exactly what is it that you think you want to know about Linear Algebra?
======
jcr
1.) My first compound question would be (as it has been in the past), "What
are some good texts? And for what levels? (beginner, intermediate, advanced?)"

For example, I've been eyeing the following two books since they're commonly
used, but of course, commonly used is not a guarantee they're any good.

James Stewart 2011 Algebra and Trigonometry 3rd Ed ISBN:0840068131

James Stewart 2011 College Algebra Concepts and Contexts ISBN:0495387894

As usual with university texts, we're dealing with the variance in "required
material" and preferred teaching style for particular courses along with the
textbook mafia exploiting the differences in opinions with multiple
overlapping titles. I wouldn't quite call the multiple versions of the same
material "cut-and-paste textbooks," but they're still really close.

Sure, I've got the luxury of revisiting fundamentals for fun even though I
don't necessarily need to revisit them again. As expected, when done, I'll
probably have my own uneducated opinion of how good those texts are at
teaching the basics, but that's beside the point -- You have the clear
advantage of having far more experience with math, and hence, you'd have a
much more informed opinion of good texts.

1.a) "Other references or resources besides textbooks?"

2.) My second question would be, "Why limit it to just `Linear Algebra`?" This
could be my own academic ignorance showing through or possibly a language
barrier of some sort, but there are so many different and useful applications
of "Algebra" that limiting it to a specific area seems, well, overly confining
and constrained.

If you're just trying to be humble and only stick to stuff you know really
well, I can empathize. There are a lot of smart math folks on HN, and some of
them know particular fields extremely well, so venturing outside of your field
of expertise can be a risky proposition. On the other hand, I know you're damn
good at a lot of different fields of mathematics, so even if you aren't _the_
resident expert of a particular field, your insights can still be very useful
and beneficial --A good example is me asking you about textbooks even though I
know you don't do the whole regular teaching thing, let alone spend your time
evaluating each new edition and variation of books for the sake of potentially
using them in a class. If someone wanted to know more about the application of
Algebraic Theory to Automata Networks, your opinion is still a hell of a lot
more informed than mine. (And no, I don't really understand it... yet!)

3.) If you want to stick to the topic of just Linear Algebra, "Where is Linear
Algebra useful?" The pure math folks are always amazing, but the engineering
types want to know how to apply the knowledge to do useful work. The first
step is simply knowing where things could be useful.

3.a) "Why is Linear Algebra useful in particular areas?"

The things you consider to be "completely elementary" or even blatantly
obvious, probably aren't. I'd bet the reason why this submission hasn't
resulted in a whole lot of questions is due to people being afraid of looking
dumb, publicly. Some of the knowledge you take for granted is actually
intimidating to others, or worse, they actually dreaded their mathematics
classes and try to avoid the topic out of fear.

[http://24.media.tumblr.com/tumblr_l0z6j5sHtL1qz7s3bo1_500.jp...](http://24.media.tumblr.com/tumblr_l0z6j5sHtL1qz7s3bo1_500.jpg)

> So, exactly what is it that you think you want to know about Linear Algebra?

If people don't know where Linear Algebra is applicable to do useful stuff,
they won't think of things that they want to know.

Without using a long string of expletives, I'm unable to express how much more
qualified you are than I am for giving answers to 3/3a.

4.) Lastly (and rhetorically), "Why do people tend to discount the things they
know?" --Even if learning math was easy for you, you still put in a lot of
effort, so you ought to give yourself more credit. :)

