I've decided to begin a series that covers the basics of linear algebra. While this isn't really supposed to replace a good book on the subject, it's more like a guide to the topics. This way, you can be informed and charming when matrix algebra comes up at your next cocktail party...
But linear algebra? Most people think of calculus when math comes up, usually along the lines of "My calculus teacher in high school was a huge jerk" or "I never really got it" and so forth. I've decided to write a little about this for a couple of reasons
- Calculus tutorials, tools, aid sheets, etc. are a dime a dozen, and there just doesn't seem to be the same level of interest in topics related to linear algebra, which I think is unfortunate
- Linalg is at least as important as calculus, if not more so. I'd argue that it's much, much more important to know these concepts for everyday life. People just don't realize that too often
- Linear algebra has a different "feel" than calculus, one that I think most people may find easier to understand. I think some concepts are more straightforward and less abstract than calculus topics. I'd hope that this means some people who wouldn't get into math maybe can with a little bit of exposure to these ideas
- A lot of linear algebra can be directly applied to computer programming topics, something also cool. In some ways, a good grounding in linear algebra will help out a whole lot if you want to learn some coding
- I love this stuff, I really do. And along with that, I feel like I have a really good grasp on the subject. If this branch of mathematics magically appeared as a beautiful woman, my fiancee should be a bit worried :)
So reading this list, particularly the second point, one may ask "Well, what is so great about this linear business that would come up in real life?". A fair question. Let me answer this question with a question: Have you ever played a video game that is in 3D? Or watched a movie with really cool CGI involving something moving? How about using Photoshop to edit photos? Perhaps you've heard of company called Google, whose PageRank algorithm has provided us with one the best search engines ever? Ok, so that's more than one question, but hopefully it makes my point. All of those things are based, at least partially, on ideas from linear algebra. Some of the concepts involved are based on ideas that even a first-year science student would understand (hint: PageRank ain't that complicated...).
Before I jump head over heels into this, I guess I should say a little bit more. First, I'm going to try to keep things conceptual, emphasizing explanation of concepts. However, it's not easy to teach math without the actual math, so I may include some hardcore stuff in these posts as well. Also, since I'm going to try to keep things as introductory as possible, I may footnote/link to more advanced topics for brevity. I'm going to assume my reader is interested in these topics (I know, a bit a stretch) and mathematically competent (or at least wanting to be). Remember that Wikipedia is a great source of background information, especially on math topics. Use The Force wisely.
I hope that makes a good case for this stuff. So, with my pleading out of the way, onwards to algebra!
