TÍCH CỦA CÁC MA TRẬN TOÀN PHƯƠNG VÔ HẠN TRÊN TRƯỜNG

Abstract

Let   be a field, and   a quadratic polynomial is given in  . We denote by   the  ring of infinite upper triangular matrices over  . A matrix   is called a quadratic matrix with respect to   if  . In this article, we will investigate the decomposition of infinite matrices in   as products of quadratic matrices with respect to  in  . Our main result states that for any positive integer k ( ), every matrix in   whose diagonal entries are equal to    can be expressed as a product of at most  quadratic matrices with respect to   in  , where   is a quadratic polynomial has two roots   This result is significant as it provides a direct derivation of a well-known theorem by Słowik (2013) and opens new directions for further research in the decomposition of infinite matrices and their applications.