In reply to Warren Kuhfeld.

Thanks for the comments. Yes, there are additional steps you can take in an attempt to "unique-ify" the eigenvectors. Unfortunately, any linear operation is a "co-dimension 1" solution that resolves most problems but leaves others unresolved. For example, suppose there are unique eigenvalues and you decide to standardize the +/- eigenvectors by returning the one that is in the same direction as some specified vector such as e_1=(1,0,...,0). That unique-ifies most vectors, but still leaves a (p-1)-dimensional subspace ("co-dimension 1") of vectors that are orthogonal to the reference vector and therefore are not uniquely resolved. The method you mention (sum of elements positive) is a linear relationship, so suffers the same drawback.

You could, of course, start iterating: if a vector is in the orthogonal complement to e_1 you can project onto e_2=(0,1,0,...,0) for the next round, etc.
But I guess I feel like these extra steps merely make the eigenvectors more arbitrary unless every numerical software package implements the same scheme.