This analysis demonstrates the generating set of elementary matrices in the odd unitary group, suggesting new insights into linear algebra.
In 1976, L.N. Vaserstein used a construction analogous to the Gram-Schmidt orthogonalisation to obtain 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 generating set for the elementary linear group.
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Ambily et al. (2026) studied this question.
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