The characterization of automorphisms of Bernstein algebras is an open
problem. We only know some particular results. Previously we have cha
racterized the automorphisms of quasiorthogonal, orthogonal, and stron
gly orthogonal weak Bernstein-Jordan algebras. In this paper we work o
n the minimal dimension with respect to quasiorthogonality, orthogonal
ity, and strong orthogonality. We establish some classification theore
ms.