Should correlation tables be half or full matrices?
For what it's worth, the convention in APA format is for the diagonals to be labelled with a dash and for the upper triangle to be left blank. See e.g. Table 1 in this paper.

Personally, I think that including redundant information in the upper triangle is wasteful and only serves to overwhelm the reader. A table formatted like a lower triangle is, at first glance, obviously a correlation matrix, while a fully-filled-in table could be anything. However, I'm not aware of any studies on the effectiveness of either method.