I've always thought of the gradient of a scalar function (id est, ##\nabla\varphi##) as being a vector field. However, I started thinking about it just now in terms of transformation with respect to coordinate changes, and I noticed that the gradient transforms covariantly. Thus, shouldn't the gradient be represented with a row vector? I don't know why this is confusing for me. After looking through a couple websites, I saw that there were some who said "yes" and some who said "no," so I don't know what to think.