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