This brief studies prime factorization problems of a multivariate polynomial matrix. We mainly investigate the LinBose problem proposed by Lin and Bose in the multidimensional system theory context. A simple proof to the Lin-Bose problem is presented in a much easier way to understand. As a by-product, we obtain some properties on modules generated by all the rows of a matrix.Index Terms-Factor prime matrix, matrix factorization, multidimensional systems, n-D polynomial matrix, polynomial ring.
Serre reduction of a system plays a key role in the theory of Multidimensional systems, which has a close connection with Serre reduction of polynomial matrices. In this paper, we investigate the Serre reduction problem for two kinds of nD polynomial matrices. Some new necessary and sufficient conditions about reducing these matrices to their Smith normal forms are obtained. ese conditions can be easily checked by existing Gröbner basis algorithms of polynomial ideals.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.