In the paper ‘Serre’s problem on projective modules over polynomial rings and algebraic K-theory’, L.N. Vaserstein and A.A. Suslin studied the freeness of projective modules over polynomial rings. For a given alternating matrix φ of size 2n, Vaserstein proved the existence of two elementary matrices of size 2n − 1 which can be modified to get symplectic matrices with respect to φ. In this talk I will define a set of matrices analogous to Vaserstein-type matrices and prove that these are elementary linear matrices. Also, we will see that under some conditions, these matrices generate Petrov’s odd elementary hyperbolic unitary group when the ring is commutative.
