Talk:System of linear equations

hi there. i edited the system of linear equations page recently because i didn't realize how unmoderated the process was. in the history list, the person who re-corrected the page said this was the place to make my comment (i hope this is the place, please correct me again if not).

i am just having to learn a lot of math and programming very fast to make up for my twenties which i spent as a musician. i am now an effects animator trying to work out a bunch of fluid dynamic stuff for a movie i am working on.

here is the content of my confusion-- line 27: "where A is an m-by-n matrix above, x is a column vector with n entries and b is a column vector with b(sub)m entries"

my understanding is that the matrix can be rectangular, i.e.: m not equal to n. if so, the column vector x should have m entries, shouldn't it?

and the vector b should have m entries too, as b(sub)m could be any float, n'est-ce pas?

any help is much appreciated.

i can't believe how great wikipedia is. better than any textbook i've been able to find, and completely community-driven/ad-free... heaven. thank you.

p.s.: sorry about the plain text, haven't yet had a chance to figure out the math formatting.

Hi, please refer to matrix multiplication. Multiplication can only happens between an m-by-n matrix and an n-by-k matrix. So if A is m-by-n then the column vector x should be n-by-1. Of course, the result matrix b is m-by-1. wshun 04:35, 13 Aug 2003 (UTC)

ok. i think i get the row/column part, but now i am confused about the equivalence. on one hand, there is the matrix representation of all the coefficients of the system, A, which has m &times n elements. on the other hand, it is stated that this can also be represented Ax=b, which seems like the whole matrix above plus one part of a matrix multiplication. if

   uh. hold on. i just got it. 

x₁ through x_n are the same on every row. (duh). and x is just those values, being multiplied by each row of the matrix of coefficients to make each value of b. ok. thanks for the help. i'll go ahead and submit this in case it helps some other equally confused person...

ok, i just read the part of the style notes that warns to talk of the article, not the subject. if someone more wiki-savvy wants to delete this talk, please do. on the bright side, a small error was fixed because of this discussion.

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Greetings and appolgies for such a mundane comment.

I notice that Daniel Brockman added some formatting to the page and I was curious about some of it.

1. Why use <em>x</em><sub >1</sub> (x₁) instead of <var>x₁</var> (x₁)?
2. Why use &minus; instead of -? The Konqueror browser has trouble with &minus;.

thanks,
Eric Blossom 19:26, 6 May 2004 (UTC)

Referring to 1, we don't use <em></em>, we use the wikimarkup, which is easier to type. And which renders as the same thing. 2- I don't know Dysprosia 22:24, 6 May 2004 (UTC)

The answer to 2 is that it looks a lot better/is clearer to read. I know there are some of these HTML characters that are 'deprecated', in the sense that they are not universally warranted.

Charles Matthews 11:09, 7 May 2004 (UTC)

Relaxation

Aren't we missing some information on relaxation methods for solving systems? (SOR, SSOR, etc.) David.Monniaux 20:37, 15 Dec 2004 (UTC)