I congratulate you on your recent edits. We need more people like you to help us editing.
Regarding the capitalizing issue, I beleive that we have to be consistent with the other parts in the linear solvers chapter as well as the general trend in the CFD literature. Vectors are a Nx1 matrix, so the reason I moved captials is to explicitly distinguish between and . We want to rule out any confusion. Since we are not out of notations, I think it will be clearer to have, at least the general form of the linear equations written with a capital Phi. Besides, the RHS is also a vector, and it is still written as capital.
(I guess that's your name, right?).
I think that the \vec is the best solution in our case. I agree with you that linear algebra texts use the notation Ax=b. While most CFD texts use Aphi=b. All in all, it doesn't matter as we are trying to offer good quality articles with as less confusion as possible. But don't you think it is better to use phi instead of x? Since all CFD people know that phi denotes a scalar variable it will be easier for them to grasp it. In any case, i am glad that our discussion was fruitful.
Here comes a third personal opinion :-) ... I've always preferd to have vectors either written in tensor notation as , or in boldface as , . A vector should always be in small caps I think. Using the \vec notation is okay for geometrical vectors but I think that it is a bit missleading for n*1 solution vectors. If we should use x or phi is a matter of taste. The reason phi is often used in CFD litterature I think is to avoid confusion with the diminsional variable x and phi is often used to denote a generic solution variable. By the way, I also think that we should add some space (not a \cdot) between the matrix and vector using \,. Then it could look like this: . This is just my $0.02. When you guys have come to an agreement please post a message about it on the forum and then if everybody else agrees add it to the format and style guide. We should probably move this discussion to the forum or to the talk page of the format and style guide. Here is an example how Eric Weinstein does in his excellent mathworld site: Mathworld on Gaussian Elimination.
--Jola 16:24, 17 December 2005 (MST)