Knowing the oritentation of the eigenvectors seems not easy?

[schwgHao]

Cause this method can only output the norms.

[osoleole]

It looses information about each components' sign. Yes, vectors direction is lost. So it is applicable only to a narrow class of tasks. Hopefully there is an easy algorithm to recover the sign. It seems this guy Terence Tao https://www.math.ucla.edu/~tao/ has a clue. He has email, and blog post about this https://terrytao.wordpress.com/2019/08/13/eigenvectors-from-eigenvalues/#comment-528850 we can ask him.

[osoleole]

By the way I found a comment in Tao's blog concerning sign

25 September, 2019 at 11:33 am
Raphael
My thoughts were along similar lines. I thought about Hückel bonding matrices and the eigenfunctions/eigenvalues emerging from that. That is pretty close to spectral graph theory. I see a major problem in that the information on the signs ist lost. That namely makes out a large bit of the unknowns. The absolut values of the components I think are not all too thrilling after all. But as I said also, group representation theory could help here out possibly.

[schwgHao]

It looses information about each components' sign. Yes, vectors direction is lost. So it is applicable only to a narrow class of tasks. Hopefully there is an easy algorithm to recover the sign. It seems this guy Terence Tao https://www.math.ucla.edu/~tao/ has a clue. He has email, and blog post about this https://terrytao.wordpress.com/2019/08/13/eigenvectors-from-eigenvalues/#comment-528850 we can ask him.

Thanks a lot for your interpretation. I would revisit here again once I have a clue.