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.