A decomposition theorem for neutrices

Abstract

Neutrices are convex subgroups of the nonstandard real number system, most of them are external sets. Because of the convexity and the invariance under some translations and multiplications, the external neutrices are models of orders of magnitude. A calculus of external numbers has been developped, which includes solving of equations, and even an analysis, for the structure of external numbers has a property of completeness. This paper contains a further step, towards linear algebra. We show that in R^{k}, with standard k, every neutrix is the direct sum of k neutrices of R. The components may be chosen orthogonal.