The Linear algebra in the quaternionic pluripotential theory

Abstract: We clarify the linear algebra used in the quaternionic pluripotential theory so that proofs of several results there can be greatly simplified. In particular, we characterize and normalize real $2$-forms with respect to the quaternionic structure, and show that the Moore determinant of a quaternionic hyperhermitian matrix is the coefficient of the exterior product of the associated real $2$-form. As a corollary, the quaternionic Monge-Amp`{e}re operator is the coefficient of the exterior product of the Baston operator.