Different Result between using PCA from toolbox and using manually programmed PCA

I try to compute PCA on my data. First, I do PCA on the data using function from toolbox. I also do PCA on the data using manual programmed function based my knowledge. First, I calculate covariance matrix of the data. Then, I find its eigenvalue and eigenvector.

PCA using function from toolbox:

[COEFF,SCORE,latent] = princomp(allData);

PCA using manually programmed function:

[V,D]=eig(cov(allData));

Both of those methods yield matrices called coefficient matrix, COEFF for the first and V for the second. Both have exactly same value, but have, sometime, different sign. Can someone explain to me?

Answer 1

[Wei Wang]

PCA enforces a sign convention on the coefficients. The largest element in each column will have a positive sign.

[Numi_Pk]

Why PCA enforces a sign convention on the coefficients?