How to overcome the arbitrary choice of signe of eigenvectors

Hello,

I vould like to average a component of an eigenvector from Matlab according to a variable parameter. The problem is that Matlab arbitrary choose the sign (+1 / -1) of eigenvectors distorting my results. (I know that they are phisically the same)

In fact, I've got my matrix A(X) that depends on a vector of variable parameters. I recover eigenvectors for several random samples of X and I want to average results. How can I overcome the changing sign of eigenvectors ?

Thank you very much for your help !

jonathan