Equivalent of Multivariate Polynomial Matrix

Jiancheng Guan; Jinwang Liu; Tao Wu; Ying Kang

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Equivalent of Multivariate Polynomial Matrix

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arxiv 2509.02574 v1 pith:PW3XMFHE submitted 2025-08-23 math.RA math.AC

Jinwang Liu , Tao Wu , Jiancheng Guan , Ying Kang This is my paper

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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.

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