Non-commutative linear algebra and plurisubharmonic functions of quaternionic variables

Abstract

We recall known and establish new properties of the Dieudonné and Moore determinants of quaternionic matrices.Using these linear algebraic results we develop a basic theory of plurisubharmonic functions of quaternionic variables. Then we introduce and briefly discuss quaternionic Monge-Ampére equations.

42 pages. A mistake in the statement of Theorem 1.2.4(iii) corrected