Why are the descriptors weighted by area before projection?

[JunzheJosephZhu]

This is the line of projection
return self.eigenvectors[:,:k].T @ (self.A @ func)
If I understand correctly, the basis itself is orthogonal, and are the solution to lambda*L@x = A@x, where L is cotangent weights and A are area weights.
So, isn't the matrix multiplication with A redundant here? Since our goal is just to project the descriptors onto a basis set for dimensionality reduction reasons.