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.