Purpose of eigenspace of covariance matrix of a blob? Given a blob of an image (representing an object), according to Wikipedia, we can compute the co-variance matrix using the image moments.

I understand that the eigenvectors of that matrix can be used to represent the principal axes of an oriented bounding box (OBB), but what are the guarantees for that particular orientation? Is the OBB the one with minimal area? And, are the eigenvectors always orthogonal?
The eigenvectors will always be orthogonal. There is no guarantee that the eigenvectors will give you the bounding box with minimal area.