Re: [Gretl-users] Principal Components Analysis: "pca" command versus "eigengen" function

Hello all again, I stick to real symmetric matrices. I think the eigengen and eigensym use different algorithms to compute eigenvectors that's why there might be differences in sign for some eigenvectors. I do not know the intrinsics of the algorithms so i cannot tell why patricular eigenvecs have the same and some have different sign. However, due to sign being non-identified "it does not matter". You must have extra information to identify depending on your purposes. The pca does not know what sign to assign. I think (correct me if i am wrong) pca uses princomp which uses eigensym and not eigengen. For example, <hansl> matrix A = (1~0.8~-0.5)|(0.8~1~0.2)|(-0.5~0.2~1) print A matrix U0 = {} eval eigengen(A,&U0) print U0 matrix U1 = {} eval eigensym(A,&U1) print U1 </hansl> or <hansl> matrix A = (1~0.8~0.25)|(0.8~1~0.4)|(0.25~0.4~1) print A matrix U0 = {} eval eigengen(A,&U0) print U0 matrix U1 = {} eval eigensym(A,&U1) print U1 </hansl> Best, Yiannis