Thread: Where do you find information about linear algebra?

Okay, I'm sorry if I'm starting to annoy anybody, but I have posted a few things about planes and hyper-planes in the mathematics section. One was how to extend Euclid's fifth postulate to higher planes of arbitrary dimensions, and the recent one was about the intersection of two planes. I have been told that instead of referring to elementary geometry I should use linear algebra to solve these problems (which makes me a little sad since I can't use my formal axiomatic system in my way). I looked at the Wikipedia page about linear algebra and it looks like it is the algebra of vectors, vector spaces, and scaling factors (numbers to multiply vectors). I have read a little bit into abstract algebra, and I've learned that there are many different types of algebras and have looked into properties of rings and groups, and now I am looking at a specific one. I have read the axioms of linear algebra and have noted their similarities and differences with elementary algebra. But that was as far as I have gotten (besides basic properties of maps and other things on that page). I've found some books on linear algebra, but no websites. Are there any websites that help?

If you Google "linear algebra" you will get links to many websites, some of which are course material.

If you Google "linear algebra" you will get links to many websites, some of which are course material.

I found a few, not very good ones (I already did the search before). It turns out that khanacademy has videos teaching linear algebra, I might have to watch them.

Originally Posted by anticorncob28

If you Google "linear algebra" you will get links to many websites, some of which are course material.

I found a few, not very good ones (I already did the search before). It turns out that khanacademy has videos teaching linear algebra, I might have to watch them.

I strongly recommend the textbook by MIT professor Gilbert Strang. It is extremely well written and quite suitable for self-learning (I tested this assertion -- the lecturer was so incompetent when I took it that the students taught themselves). The one exception is the chapter on determinants, but that's a minor blemish.

If you can find a copy of the Strang book, buy it. You won't be disappointed.

I strongly recommend the textbook by MIT professor Gilbert Strang. It is extremely well written and quite suitable for self-learning (I tested this assertion -- the lecturer was so incompetent when I took it that the students taught themselves). The one exception is the chapter on determinants, but that's a minor blemish.

If you can find a copy of the Strang book, buy it. You won't be disappointed.

Thanks for the suggestion. I would buy it with my own money because, you see I am 15 and my parents still buy me stuff (lol) and they don't appreciate maths, and certainly have no extensive knowledge about it, and probably wouldn't be willing to pay $60 or so for a book about elementary linear algebra. I hardly ever spend money though. I've heard from mathsy people that linear algebra was the hardest course they ever took, so if I can get past that I can hopefully be assured to get the best maths education I can, because I want a PhD and I am a little worried that some day I'll just let go and things will get too complex for me to understand.

Originally Posted by anticorncob28

I strongly recommend the textbook by MIT professor Gilbert Strang. It is extremely well written and quite suitable for self-learning (I tested this assertion -- the lecturer was so incompetent when I took it that the students taught themselves). The one exception is the chapter on determinants, but that's a minor blemish.

If you can find a copy of the Strang book, buy it. You won't be disappointed.

Thanks for the suggestion. I would buy it with my own money because, you see I am 15 and my parents still buy me stuff (lol) and they don't appreciate maths, and certainly have no extensive knowledge about it, and probably wouldn't be willing to pay $60 or so for a book about elementary linear algebra. I hardly ever spend money though. I've heard from mathsy people that linear algebra was the hardest course they ever took, so if I can get past that I can hopefully be assured to get the best maths education I can, because I want a PhD and I am a little worried that some day I'll just let go and things will get too complex for me to understand.

There are online sellers who charge under $20 for new, international editions. Used ones cost even less. In a quick google search, I found several vendors willing to sell older editions for less than $10, shipped.

Also, I'm a bit surprised that your math friends claimed that linear algebra was the most difficult course for them. It's actually very straightforward stuff (the "linear" part is key). Trust me, there are far more abstruse and intellectually challenging branches of mathematics! In terms of broad utility, linear algebra is hard to beat. Differential and integral calculus, linear algebra, differential equations, stochastics/probability and complex analysis will get you pretty far in science and engineering.

Also, I'm a bit surprised that your math friends claimed that linear algebra was the most difficult course for them.

Okay, that was a bit of a baseless claim. I did see one person here on the other linear algebra thread that was posted recently saying that it was the hardest class for them at their time, probably because it was so different from the other math classes they were taking. One person on Yahoo answers asked what the most advanced area of math was, and suggested calculus (I think I saw that when I was 12. I did know a few basic calculus concepts at the time, but now, looking back, I laugh at the thought that calculus is the most advanced area of math. Just wow. lol). One person stated linear algebra (which I now know is not true) that it is "extremely tough". It probably is for average people, but maybe not so for people who have a mind for mathematics.

Here is a sort of unrelated personal note on algebras in general that might be helpful.Algebra can be as easy as a tic-tac-to game.Starting with math is formed from logic.Logic is the comparison of two objects or things.A measurment against a known object or standard.Sort of like weights and balances.Math is the mumerical expression of logic.Each object has a set quantity of numbers attached to it.It is very precise.Algebra is the logic used in arithmetic.The same arithmatic you learned in grade school.They should teach algebra before arithmetic,or better yet logic (Venn style)before any math or science.

Originally Posted by Pot Raost

Logic is the comparison of two objects or things.

No it's not.

They should teach algebra before arithmetic

Until you've done arithemetic you don't know what numbers are or the rules for their operation.

I'd be interested to see the results of teaching abstract algebra (where you forget about little things like numbers) before teaching arithmetic, but I doubt it'd really work since the easiest way to get across some of the points of abstract algebra is to refer back to existing models, like natural or real numbers.

For just algebra though, I have to agree with Dywyddyr. How exactly are you going to make sense of "2*x + 3 = y, solve for x" if you don't know what + means.

Edit: BTW, logic is the comparison of two very specific things: True and False. :P

Originally Posted by anticorncob28

I've found some books on linear algebra, but no websites. Are there any websites that help?

I'd recommend a graphing calculator for linear algebra. I use a TI-92, and it can perform operations on matrices and do just about anything else. Spreadsheets should be useful too in the study of linear algebra. You can calculate determinants quickly and easily using cell formulas.

Jagella

Logic is an algebra performed on the truth values of a set of statements.
Graphing calculators have little to do with understanding math.
Here is some Strang on video;
Linear Algebra | Mathematics | MIT OpenCourseWare

There are free linear algebra courses at Utube. Just search for "Linear Algebra". (MIT course is highly recommended. Look for "MIT Linear Algebra Spring 2005"). Also there's a free book from Jim Hefferon here: http://joshua.smcvt.edu/linearalgebra/book.pdf It is a nice instruction in linear algebra.