On the Odd Unitary Analogue of Gram-Schmidt Process

Abstract

In 1976, L.N. Vaserstein used a construction analogous to the Gram-Schmidt orthogonalisation, for obtaining a set of symplectic matrices from a set of elementary matrices. We have a similar construction for Petrov's odd unitary group. Here, we prove that the elementary matrices in the odd unitary analogue of the Gram-Schmidt process form a set of generators for the elementary linear group.