>David C. Ullrich <email@example.com> wrote in message news:<firstname.lastname@example.org>... >> On 22 Apr 2004 15:44:12 -0700, Anonymous wrote: >> >> >I'm currently a math major and am taking linear algebra, but I'm in >> >serious danger of failing. I just don't get it! Is this newsgroup a >> >place to come to ask questions and get information about learning >> >math? Or is there somewhere more appropriate to go? I've always had >> >trouble with vectors, and I think I fell apart sort of right at the >> >beginning of linear algebra (although, I did manage to get a B- on the >> >very first exam). I've got another exam next week. What can I do? I >> >don't get all the terms, concepts, and jargon. Anyone know how to >> >make learning linear algebra easier and more practical? Anyone got >> >any practice problems? > >Thanks for the post. I've read it all the way through and agree and >understand what you're saying. About the definitions, I like your >definition for "basis": "independent spanning set" because it's short >and simple. Therefore, it's *easy* to memorize. My text book would >tend to defend the basis in a really, really abstract way like: "Let S >[contained in symbol] V be a subset of V. If *x* [element symbol] S = >a1x1 + a2x2 + ... + a^nx^n = *0*, then *x* is a basis if a^i (1 < i < >n) = 0 for all a^i and Span(V) = S.", or something really wordy and >convoluted like that. I mean, I eventually understand what the >definition is saying. But, "independent spanning set" is just so much >easier, IMO.
Glad you liked the definition. The only reason it seemed simpler than the definition in the book is that I didn't define the words "independent" and "spanning".
Here's the deal with definitions. But it only works if you know them _exactly_ right, including the wordy convoluted ones. If you take "independent spanning set" and insert the defintions of "independent" and "spanning" you'll get the definition of "basis" in the book.