On the Odd Unitary Analogue of Gram-Schmidt Process

2025/05/22 by A. A. Ambily, A., Ambily A., A. K. +1
Computer Science · Mathematics · #13A99 #14L35 #15A24 (secondary) #20G99 (primary) #FOS: Mathematics #Group Theory (math.GR) #K-Theory and Homology (math.KT) #Matrix Theory and Algorithms #Random Matrices and Applications #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2505.16295

openalex publication_date 2025/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Visualization for Petrov's Odd Unitary Group
• The E-normal structure of Petrov's odd unitary groups over commutative rings
• The E-normal structure of odd dimensional unitary groups

Related

• Gram-Schmidt-Vaserstein generators for odd sized elementary groups
• Visualization for Petrov's Odd Unitary Group
• Exponentiation and decomposition formulas for common operators 1: Classical applications
• Special orthogonal, special unitary, and symplectic groups as products of Grassmannians
• On the characteristic map of finite unitary groups