On the Odd Unitary Analogue of Gram-Schmidt Process

TL;DR

This paper extends the Gram-Schmidt process to the odd unitary group, showing that elementary matrices generated through this process form a generating set for the elementary linear group.

Contribution

It introduces an odd unitary analogue of the Gram-Schmidt process and proves the elementary matrices form a generating set for the elementary linear group.

Findings

Elementary matrices generate the elementary linear group.

The construction is analogous to Vaserstein's symplectic case.

Provides a new tool for studying odd unitary groups.

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.