arXiv subjects

Jiancheng Guan

Publications and source records attributed to Jiancheng Guan.

3 recordsLinked to original sources

arXiv2026

Smith Form Equivalence for Several Classes of Multivariate Polynomial Matrices

This paper investigates the equivalence reduction for several classes of multivariate polynomial matrices and their Smith forms, establishing some criteria for such reduction. In particular, we employ algebra isomorphisms as a key tool to study this equivalence problem. We then leverage the Quillen-Suslin and Lin-Bose theorems to extend these results to non-square and rank-deficient matrices. Moreover, the verification of our criteria is achievable algorithmically via existing Gröbner basis methods.

math.AC↗

arXiv2025

Equivalent of Multivariate Polynomial Matrix

The equivalence of multidimensional systems is closely related to the reduction of multivariate polynomial matrices, with the Smith normal form of matrices playing a key role. So far, the problem of reducing multivariate polynomial matrices into Smith normal form has not been fully solved. This article investigates the Smith normal form of quasi weakly linear multivariate polynomial matrices. Breaking through previous limitations, providing sufficient and necessary conditions.

math.RA↗

arXiv2024

Further results on equivalence of multivariate polynomial matrices

This paper investigates equivalence of square multivariate polynomial matrices with the determinant being some power of a univariate irreducible polynomial. We first generalized a global-local theorem of Vaserstein. Then we proved these matrices are equivalent to their Smith forms by the generalized global-local theorem.

math.AC↗