Products of infinite upper triangular quadratic matrices

Let Fbe a field and q(x) a quadratic polynomial in F[x] with q(0) not equal 0. We denote by T-infinity(F) the algebra of all infinite upper triangular matrices over the field F. A matrix A is an element of T-infinity(F) is called a quadratic matrix with respect to q(x) if q(A) = 0. In this paper, we first investigate the subgroup in T-infinity(F) generated by all quadratic matrices with respect to q(x) and then present some applications. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.