With a table showing correlations between several variables, one must choose whether to show values in only ~half the cells (and if so, then choose above or below the diagonal) or all the cells. Since correlation is a symmetric measure, the same amount of information is conveyed with both options.
Filling the whole matrix might make it easier for people to find a particular value, because they can think of either one as primary and look for it in either part of the matrix. However, filling the whole matrix might make the presentation more overwhelming to a reader ("wow, that's a lot of numbers") while the half matrix might seem more elegant.
Has there been any work done looking at which is more effective for communication?
Are there widely used style guides in certain fields that answer this question, which might provide a starting point for a field which lacks such a guide?